SOLUTION: Question A company claims that 80% of its trainees are promoted within the first year. Find the probabilities among 8 randomly selected trainees. 1. At least 6 will be promoted.

Question 1058353: Question
A company claims that 80% of its trainees are promoted within the first year. Find the probabilities among 8 randomly selected trainees.
1. At least 6 will be promoted.
2. From 5 to 7 will be promoted
3. At most 6 will be promoted.
4. None will be promoted
Question
During rush periods, accidents happen in Nicosia at a rate of 2 per hour. The morning rush period lasts for 1 hour 30 minutes, and the evening rush period for two hours.
1. What is the probability that there will be no accidents during the morning rush period?
2. What is the probability of 2 accidents during the evening?
3. What is the probability of four or more accidents during the morning?
4. What is the probability that there will be no accidents during both the morning and evening rush period?
Question
We have the following data:
y x
6.2 12.3
8 13.7
8.4 14.5
5.3 11.2
7.2 13.2
8.7 14.1
5.7 12
Calculate the following:
1. Means
2. Variances and Standard deviations
3. Correlation coefficient
4. Find the regression(least square)estimator
5. Use the regression to predict Y when x=5

Question
A. We have collected data for the absences of 50 students with days of the week:
Monday Tuesday Wednesday Thursday Friday
Absences 14 7 4 9 16
Test if the absences are equally distributed over all days of the week (critical value=6.251).
B. The following table shows the effect on three types of inhalers that helps people breathing who suffer from asthma.
Type of inhaler
Result A B D
Recovery 25 15 21
No effect 36 10 13
Test whether there is no association between the type of inhaler and the effect (value=7.815).
Question
It has been found that the times taken by people to complete the income tax form follows a Normal distribution with a mean of 100 minutes and a standard deviation of 20 minutes.
Calculate the following probabilities:
1. A person takes 110 minutes or more to complete the form
2. A person takes between 100 and 125 minutes to complete the form
3. A person takes between 75 and 115 minutes to complete the form
4. A person takes less than 120 minutes to complete the form

Question
A company claims that 80% of its trainees are promoted within the first year. Find the probabilities among 8 randomly selected trainees.
1. At least 6 will be promoted.
2. From 5 to 7 will be promoted
3. At most 6 will be promoted.
4. None will be promoted
Question
During rush periods, accidents happen in Nicosia at a rate of 2 per hour. The morning rush period lasts for 1 hour 30 minutes, and the evening rush period for two hours.
1. What is the probability that there will be no accidents during the morning rush period?
2. What is the probability of 2 accidents during the evening?
3. What is the probability of four or more accidents during the morning?
4. What is the probability that there will be no accidents during both the morning and evening rush period?
Question
We have the following data:
y x
6.2 12.3
8 13.7
8.4 14.5
5.3 11.2
7.2 13.2
8.7 14.1
5.7 12
Calculate the following:
1. Means
2. Variances and Standard deviations
3. Correlation coefficient
4. Find the regression(least square)estimator
5. Use the regression to predict Y when x=5

Question
A. We have collected data for the absences of 50 students with days of the week:
Monday Tuesday Wednesday Thursday Friday
Absences 14 7 4 9 16
Test if the absences are equally distributed over all days of the week (critical value=6.251).
B. The following table shows the effect on three types of inhalers that helps people breathing who suffer from asthma.
Type of inhaler
Result A B D
Recovery 25 15 21
No effect 36 10 13
Test whether there is no association between the type of inhaler and the effect (value=7.815).

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
1. 8C6(.8^6)(.2^2)=0.2936
8C7(.8^7)(.2)=0.3355
8C8(.8^8)=0.1678
Sum is 0.7969.
2. 8C5(.8^5)(.2)^3=0.1468
Add in the above two for 6 and 7 and the total is 0.7759
3.At most 6 means everything but 7 and 8, whose collective sum is 0.5033. The probability is the complement or 0.4967.
-------------------------------
Poisson distribution and parameter is proportional to time
Morning rush hour would have a parameter equal to 2*1.5 or 3
probability of no accidents is e^(-3)*3^0/0!=e^(-3)=0.0498.
------------------------------
Here the parameter is 2*2 or 4. and we want x=2. It is e^(-4)*4^2/2=0.1465.
------------------------------
Find probability of 0,1,2,3 accidents in the morning.
for 0 it is 0.0498
for 1 it is 3 times that or 0.1494
for 2 it is e^(-3)*3^2/2=0.2240
for 3 it is e^(-3)*27/6=0.2240.
total is 0.6473, so complement and answer is 0.3527.
----------------------------
Morning probability is 0.0498. Evening is 0.0183. Joint probability is 0.0009

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