SOLUTION: Pls need solution with step by step working for the questions 1.An aerospace company has submitted bids on two separate federal government defense contracts. The company preside

Question 1196465: Pls need solution with step by step working for the questions
1.An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 57% probability of winning the first contract. If they win the first contract, the probability of winning the second is 67%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 44%.
What is the probability that they lose both contracts?

3 points
QUESTION 3
1. An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 58% probability of winning the first contract. If they win the first contract, the probability of winning the second is 55%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 29%.
Given that they win the second contract, what is the probability that they win the first one?

FP(W)=58/100
=
3 points
QUESTION 4
1. An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 46% probability of winning the first contract. If they win the first contract, the probability of winning the second is 66%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 39%.
What is the probability that they win both contracts?

P(W and W)= 0.46 * 0.66
= 0.3036
3 points
QUESTION 5
1. An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 37% probability of winning the first contract. If they win the first contract, the probability of winning the second is 73%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 37%.
What is the probability that they win the second contract?

3 points
QUESTION 6
1. An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 54% probability of winning the first contract. If they win the first contract, the probability of winning the second is 66%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 22%.
Are the results of the two bids independent? If yes, enter 1. If no, enter 0.

3 points
QUESTION 7
1. An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 67% probability of winning the first contract. If they win the first contract, the probability of winning the second is 53%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 35%.
What is the probability that they lose only one contract?

3 points
QUESTION 8
1. An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 64% probability of winning the first contract. If they win the first contract, the probability of winning the second is 50%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 28%.
What is the probability that they win at least one of the contracts?

3 points
QUESTION 9
1. A certain type of tomato seed germinates 32% of the time. A backyard farmer planted 10 seeds.
What is the probability that 2 or fewer germinate?

4 points
QUESTION 10
1. A certain type of tomato seed germinates 31% of the time. A backyard farmer planted 10 seeds.
What is the probability that 3 or more germinate?

4 points
QUESTION 11
1. The number of students who seek assistance with their statistics assignments is Poisson distributed with a mean of 0.29 per day.
What is the probability that at least three students seek assistance in 13 days?

4 points
QUESTION 12
1. The number of students who seek assistance with their statistics assignments is Poisson distributed with a mean of 0.24 per day.
What is the probability that 3 students seek assistance in 26 days?

4 points
QUESTION 13
1. The time (in minutes) between telephone calls at an insurance claims office has the following exponential distribution.
f(x)=0.13e-0.13x, x≥0
What is the probability of the time between telephone calls being between 1.2 and 5.1 minutes?

4 points
QUESTION 14
1. The time (in minutes) between telephone calls at an insurance claims office has the following exponential distribution.
f(x)=0.28e-0.28x, x≥0
What is the mean time (in minutes) between telephone calls?

4 points
QUESTION 15
1. The long-distance calls made by the employees of a company are normally distributed with a mean of 6 minutes and a standard deviation of 2 minutes.
What is the length of time (in minutes) that exceeds 59% of the length of the calls by the employees?

4 points
QUESTION 16
1. The long-distance calls made by the employees of a company are normally distributed with a mean of 6 minutes and a standard deviation of 2 minutes.
Find the probability that a call lasts more than 5.5 minutes.

4 points
QUESTION 17
1. The marks on a statistics midterm test are normally distributed with a mean of 78 and a standard deviation of 6.
What is the grade that is exceeded by 63% of the average midterm mark for a class of 36?

4 points
QUESTION 18
1. The marks on a statistics midterm test are normally distributed with a mean of 78 and a standard deviation of 6.
What is the probability that a class of 36 has an average midterm mark that is more than 77.38?

4 points
QUESTION 19
1. Consider the population of electric usage per month for houses. The standard deviation of this population is 227 kilowatt-hours. What is the smallest sample size to provide a 90% confidence interval for the population mean with a margin of error of 44 or less? (Enter an integer number. Do not round any number in your intermediate calculations.)

4 points
QUESTION 20
1. In order to estimate the average electric usage per month, a sample of 100 houses was selected and the electric usage was determined. The sample mean is 1086 KWH. Assume a population standard deviation of 215 kilowatt hours.
At 92% confidence, compute the lower bound of the interval estimate for the population mean.

4 points
QUESTION 21
1. A production line operation is designed to fill a container with a mean weight of 20 ounces. A quality control inspector selects a random sample of 100 containers to test whether overfilling or underfilling is occurring in the production line because if so, the line should be shut down and adjusted to obtain proper filling. The sample provided an average mean filling weight of 20.13 ounces. From past data, a standard deviation of 2 ounces is assumed for the population of filling weights. Let μ denote the mean filling weight in ounces for this production line.
What is the value of the appropriate test statistic to perform this test?

3 points
QUESTION 22
1. Data from the Census Bureau states that the mean age at which women in the United State got married in 2010 is 26. A new sample of 1000 recently wed women provided their age at the time of marriage. We would like to test whether the data from this new sample indicate that the mean age of women at the time of marriage exceeds the mean age in 2010. From past data, a standard deviation of 5 years is assumed for the population of interest. The value of the appropriate test statistic (z) is computed for the sample and it's equal to 0.10.
What is the p-value for this test?

4 points
QUESTION 23
1. A production line operation is designed to fill a container with a mean weight of 20 ounces. A quality control inspector selects a random sample of 100 containers to test whether overfilling or underfilling is occurring in the production line because if so, the line should be shut down and adjusted to obtain proper filling. From past data, a standard deviation of 2 ounces is assumed for the population of filling weights. The value of the appropriate test statistic (z) is computed for the sample and it's equal to -1.36.
What is the conclusion of the test using a 0.1 level of significance?
Enter 1 if the overfilling or underfilling is occurring in the production line.
Enter 0 if overfilling or underfilling is NOT occurring in the production line.

Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

You posted way too many questions.
The official rule is one question per post.
Sometimes, if the questions are fairly short, then a few can be squeezed in together (which is useful if they are related questions). Though in my opinion it's better to stick to the official rule.

I'll do question 1 to get you started.

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Question:
1.An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 57% probability of winning the first contract. If they win the first contract, the probability of winning the second is 67%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 44%.
What is the probability that they lose both contracts?

Solution:
There's a 57% chance of getting the first contract.
That means there's a 100% - 57% = 43% chance of not winning the first contract.
This converts to the decimal form 0.43

It states that if the first contract is lost, then the probability of winning the second contract is 44%
So there's a 100% - 44% = 56% chance of losing the second contract if the first contract was lost.
This converts to the decimal form 0.56

Multiply those decimal values to get 0.43*0.56 = 0.2408 = 24.08% which is the probability of losing both contracts in a row.

Edit: @ikleyn makes a good point about independent vs dependent events. However, I'm using the idea that P(A and B) = P(A)*P(B given A). So multiplication is still valid here.

Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
1. An aerospace company has submitted bids on two separate federal government defense contracts.
The company president believes that there is a 57% probability of winning the first contract.
If they win the first contract, the probability of winning the second is 67%.
However, if they lose the first contract, the president thinks that the probability
of winning the second contract decreases to 44%.
What is the probability that they lose both contracts?
~~~~~~~~~~~~~~~~~

            When I read the solution by @math_tutor2020, everything looks good,
            but then I read the last line, where he multiplies the individual loosing probabilities,
            as if these events are independent - which is not obvious for me.

            Therefore, I developed another solution. It produces the same answer,
            but, at least, withdraws the question about independency of loosing events.

P(win 1st contract) = P(1) = 0.57 (given). P(lose 1st contract) = 1 - 0.57 = 0.43 (the complement). P(win 2nd contract) = P(2) = 0.57*0.67 + (1-0.57)*0.44 = 0.5711. P(win both 1st and 2nd contracts) = 0.57*0.67 = 0.3819. P(win at least one of the two contracts) = P(1) + P(2) - P(both) = 0.57 + 0.5711 - 0.3819 = 0.7592. P(lose both) = 1 - P(win at least one of the two contracts) = 1 - 0.7592 = 0.2408 = 24.08%. ANSWER

Solved.

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