Question 603930: 7. The manager of a clothing store wishes to analyze the relationship between the type of customer and the form of payment made. The following data has been collected for 1010 customers.
Customer Credit Card Check Cash Total
Male 296 104 207 607
Female 188 170 45 403
Total 484 274 252 1010
If a customer is selected at random from this group, find the following probabilities. Round your answer to a three place decimal (.123).
a) The customer is a male.
b) The customer paid by credit card.
c) The customer paid by check, given that she is a female.
d) The customer did not pay by credit card.
e) The customer is a male, given that he paid by cash.
f) The customer is a female and she paid by credit card.
g) The customer is a male or the customer paid by cash.
10. Assume that a researcher randomly selected 10 newborn babies and counts the number of girls selected, as x. The probability corresponding to the 10 possible values of x are summarized in the table below. Complete the probability distribution and complete the following questions. Write the mean and standard deviation with a one place decimal and write the probabilities as a three place decimal (.123).
x p(x) x•p(x) x2 •p(x)
0 0.000 0.000 0.000
1 0.001 0.001 0.001
2 0.007 0.014 0.028
3 0.024 0.072 0.216
4 0.062 0.248 0.992
5 0.113 0.565 2.825
6 0.183 1.098 6.588
7 0.209 1.463 10.241
8 0.183 1.464 11.712
9 0.122 1.098 9.882
10 0.096 0.960 9.600
a) Using the formula for the mean of a probability distribution find the average number of baby girls for this distribution.
b) Find the standard deviation.
c) Find the probability of selecting at least 5 girls.
d) Find the probability of selecting at most 7 girls.
e) Use the mean the standard deviation from above and the rule of thumb to find the maximum and minimum number of girls out of the 10 newborn babies. Determine whether a nursery containing 8 baby girls is usual or unusual. Write usual or unusual in the answer text box.
11. A pediatrician finds that about 15% of the infants now injected with the MMR vaccine, as required by law in many states, develop some form of minor reactions. If the doctor intends to inject 400 infants during the year with this vaccine:
a) About how many can be expected (µ=np) to develop any form of a reaction.
b) Find the standard deviation.
c) What is the probability that out of the 400 infants, exactly 25 will develop a reaction? Write your answer as a decimal.
12. If z is a standard normal variable, find the probabilities below. Write your answer as a four place rounded decimal.
a) The probability that z is greater than -1.82.
b) p(-0.73 < z < 2.27)
c) p(z < 2.01)
Question 13
13. Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Complete the following, write your answer as a four place rounded decimal (.1234).
a) Find the probability that a randomly chosen woman has a height greater than 60 inches.
b) If 100 women are randomly selected, find the probability that they have a mean height between 63.5 inches and 64.5 inches. Use the central limit theorem.
14. Given the data below, find the mean of the original three samples. List the different possible samples taking two at a time, find the mean of each of them and then find the overall population mean of the 9 samples. How does the sample mean compare with the population?
Personal phone calls received in the last three days by a new employee were 3, 5, and 6. Assume that the samples of size 2 are randomly selected with replacement from this population of three values.
15. A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval. Indicate the following values.
a) p-hat rounded to three decimal places
b) q-hat rounded to three decimal places.
c) margin of error, E =
d) confidence interval: < p <
16. If an additional survey is to be completed, how large of a sample must be taken to be 99% confident that the estimate is within 2% of the true proportion of voters? Round the answer to the nearest whole number. n =
17. A random sample of 94 light bulbs had a mean life of 587 hours with a standard deviation of 36 hours. Construct a 90% confidence interval for the mean life of all light bulbs of this type.
a) Find the margin of error, E= Round to tenths place.
b) Confidence Interval: Round the tenths place. < µ <
18. Use the given degree of confidence and the sample data below to construct a confidence interval for the population mean. Assume that the population is normally distributed and round your answers to one decimal place.
The principal randomly selected six students to take an aptitude test.
There scores were:
83.0 84.1 83.5 83.7 84.1 73.5
Determine a 90% confidence interval for the mean score of the six students.
a) sample mean =
b) standard deviation =
c) margin of error, E =
d) 90% confidence interval: < µ <
19. Assume that a simple random sample has been selected from a normally distributed population. State the null hypothesis, the alternate hypothesis, the test statistic, the p-value, the critical value and state the conclusion.
Test the claim that the mean lifetime of a car engine of a particular type is greater than 220,000 miles. Sample data are summarized as n=23, mean = 226,450 miles, the population standard deviation,
= 11,500 miles. Use a z-test and a significance level of 0.01.
a) Ho: µ < miles.
b) Ha: µ > miles.
c) test statistic z = Round to two decimal places.
d) p-value = Round to four decimal places.
e) Write reject or do not reject the null hypothesis.
f) Conclusion: There is or is not sufficient evidence to show that the lifetime of the car engine is greater than 220,000.
20. Assume that a hypothesis test of the given claim will be conducted. Identify the type I error for the test.
The principal of a middle school claims that test scores of the seventh-graders at his school average less than the test scores of seventh graders at a neighboring school, which has an average described by a mean = 74.7.
Answer
a. The error of failing to reject the claim that the mean is less than 74.7 when it actually is equal to 74.7.
b. The error of rejecting the claim that the mean is less than 74.7 when it actually is equal to 74.7.
c. none of the above
d. The error of rejecting the claim that the mean is less than 74.7 when it is actually is less than 74.7.
Answer by stanbon(75887)   (Show Source):
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