1. An aptitude test was given to a random sample of 228 people intending to become data-entry clerks. The results are shown below, where x is the score on a 10-point scale and f is the frequency of people with this score.

x 1 2 3 4 5 6 7 8 9 10 f 9 21 46 51 42 18 12 10 8 5

Assume that these data represent the entire population of people intending to become data-entry clerks.(a) Use the relative frequencies to find P(x) for x = 1 to x = 10. (b) Compute the probability that x is between 2 and 5 (including 2 and 5).(c) Compute the probability that x is less than 3.(d) Compute the expected value of the x distribution.(e) Compute the standard deviation of the x distribution.

2. The management of a restaurant conducted a survey and found that 28% of the customers preferred to sit in the smoking section. Based on this information, what is the probability that for a random sample of 12 customers, 3 preferred the smoking section?

3.Of all college freshmen who try out for the track team, the coach will only accept 30%. If 15 freshmen try out for the track team, what is the probability that(a) all 15 are accepted?(b) at least 8 are accepted?(c) no more than 4 are accepted?(d) between 5 and 10 are accepted (including 5 and 10)?

4. The president of a bank approves 68% of all new applications. What is the expected number of approvals if 75 loan applications are chosen at random?

5.Past records show that the probability of catching a lake trout over 15 pounds at Talston Lake (Canada) is about 20% for each full day a person spends fishing. What is the minimal number of days a person must fish to be at least 89.3% sure of catching one or more lake trout over 15 pounds?

6. We are interested in when the first odd number will occur for repeated rolls of a balanced die. What is the population mean for this geometric distribution (i.e., the expected number of rolls for the first odd number to occur)?

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7.According to the empirical rule, for a distribution that is symmetric and bell-shaped, approximately _______ of the data values will lie within 1 standard deviation oneach side of the mean.8.Assuming that the weights of newborn babies at a certain hospital are normally distributed with mean 6.5 pounds and standard deviation 1.2, how many babies in a group of 80 fromthis hospital are expected to weigh more than 8.9 pounds?9.Let x be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam's sociology class. After interviewing many students, it was found that x has an approximately normal distribution with mean = 6.8 hours and standard deviation = 2.1 hours.

Convert each of the following x intervals to standardized z intervals.(a) x 7.5 (b) 5 x 8(c) x 4

Convert each of the following z intervals to raw-score x intervals.(d) z 2(e) 0 z 2(f) z 3

10.Operating temperatures of two models of portable electric generators follow a normal distribution. For generator I, the mean temperature is 1 = 148F with standard deviation 1 = 25F. For generator II, the mean temperature is 2 = 143F with standard deviation 2 = 8F. At peak power demand, generator I was operating at 166F, and generator II was operating at 165F.

(a) At peak power output, both generators are operating at about the same temperature. Relative to the operating characteristics, is one a lot hotter than the other? Explain.

(b) Convert the peak power temperature for each generator to standard z units. Then locate both z scores under a standard normal curve. Could one generator be near a meltdown? Which one? Explain your answer.

11.Weights of a certain model of fully loaded gravel truck follow a normal distribution with mean = 6.4 tons and standard deviation = 0.3 ton. What is the probability that a fully loaded truck of this model is

(a) less than 6 tons?

(b) more than 7 tons?

(c) between 6 and 7 tons?

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12.Quality-control studies for Speedy Jet computer printers show that the lifetime of the printer follows a normal distribution with mean = 4 years and standard deviation = 0.78 years. The company will replace any printer that fails during the guarantee period. How long should Speedy Jet printers be guaranteed if the company wishes to replace no more than 10% of the printers?

13.A random sample of 14 evenings (6 to 9 P.M.) at the O'Sullivan household showed the family received an average of x = 5.2 solicitation phone calls each evening. The sample standard deviation was s = 1.9.

(a)Find a 95% confidence interval for the population mean number of solicitation calls this family receives each night.

(b)Write a brief explanation of the meaning of the confidence interval in the context of this problem.

14. Jordan is the manager of a used book store. He wants to estimate the average amount a customer spends per visit. A random sample of 80 customer receipts gave a mean of x = $6.90 with standard deviation s = $2.45.

(a) Find a 90% confidence interval for the average amount spent by all customers.

(b) What conditions are necessary for your calculations?

(c) For a day when the book store had 80 customers, use part (a) to estimate a range of dollar values for the total income on that day.

15.Mr. Crandall has assigned a term paper due at the end of the semester. He would like to know the average length of the paper. The data below are the numbers of typed pages from a random sample of 10 term papers. Use these data to create a 95% confidence interval for the population mean length of all term papers for his class.

14 20 25 10 16

8 15 12 18 9

16.Computer Depot is a large store that sells and repairs computers. A random sample of 110 computer repair jobs took technicians an average of x = 93.2 minutes per computer. Assume that is known to be 16.9 minutes.

(a)Find a 99% confidence interval for the population mean time for computer repairs.

(b)Write a brief explanation of the meaning of the confidence interval in the context of this problem.

17.A random sample of 56 credit-card holders showed that 41 regularly paid their credit-card bills on time.

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BAUD 303 Final Exam

(a) Let p represent the proportion of all people who regularly paid their credit-card bills on time. Find a point estimate p for p.

(b) Find a 95% confidence interval for p.

(c) What assumptions are required for the calculations of part (b)? Do you think that these assumptions are satisfied? Explain.

(d) How many more credit-card holders should be included in the sample to be 95% sure that a point estimate p will be within a distance of 0.05 from p?

18.Long-term experience shows that after laser eye surgery, the mean recovery time is = 5.3 days. However, a random sample of 32 patients with this surgery had a sample mean recovery time of x = 4.2 days.

(a)Does this indicate that the mean recovery time is dropping? Use a 1% level of significance. Assume = 1.9 days.

(b) What is the level of significance? State the null and alternate hypotheses. Will you use a lefttailed, right-tailed, or two-tailed test?

(c) Identify the sampling distribution you will use: the standard normal or the Student's t. Explain the rationale for your choice. What is the value of the sample test statistic?

(d) Find (or estimate) the P value. Sketch the sampling distribution and show the area corresponding to the P value.

(e) Based on your answers for parts (a) to (c), will you reject or fail to reject the null hypothesis? Interpret your decision in the context of the application.

19.A small electronics store has begun to advertise in the local newspaper. Before advertising, the long-term average weekly sales were $9,820. A random sample of 50 weeks while the newspaper ads were running gave a sample mean weekly sales of x = $10,960.

(a)Does this indicate that the population mean weekly sales is now more than $9,820? Test at the 5% level of significance. Assume = $1,580.

(b) State the null and alternate hypotheses.

(c) Compute the z or t value of the sample test statistic.

(d) Find the P value or an interval containing the P value for the sample test statistic.

(e)Based on your answers for parts A-C, what is your decision?(1)Do not reject H0(2) Reject H0(3) Cannot determine