STAT_170 exam 2

National Weather Service records show that over a 30-year period, the annual precipitation in Atlanta, Georgia, had an approximately normal distribution with a mean of 49.8 inches and a standard deviation of 7.6 inches. What is the probability that in a randomly selected year, it will have precipitation more than 52 inches?

0.386

National Weather Service records show that over a 30-year period in Atlanta, Georgia, the annual temperature had a mean of 62.2 degrees Fahrenheit with a standard deviation of 1.3 degrees. The margin of error associated with the 90% confidence interval for the mean annual temperature of in Atlanta is

0.403

According to thepoultrysite.com, the weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1387 grams and standard deviation 161 grams. What is the probability that a randomly selected broiler weighs between 1200 and 1500 grams?

0.636

The total area or probability under a standard normal curve is

1

A 85% confidence interval for the mean time, in minutes, spent by the employees of a company to get to the work is found to be (25 hours, 45 hours). The margin of error for the 85% CI for the mean time is

10 hours

Scientists what to estimate the mean weight of mice after they have been fed a special diet. From previous studies, it is known that the weight is normally distributed with a variance of 9. How many mice must be weighed so that a 95% confidence interval of mean weight will have a margin of error of 0.5 grams?

139

Scores on a university exam are Normally distributed with a mean of 78 and a standard deviation of 8. What percent of students score below 70?

15.9%

A violin student records the number of hours she spends practicing during each day. Suppose the number of hours spent follows a normal distribution with mean 1.3 hours and standard deviation 15 minutes. Find the standardized score z for X = 2 hours using the formula Z = ( X − μ ) σ .

2.8

Steel rods are manufactured with a mean length of 25 centimeter (cm). Because of variability in the manufacturing process, the length of the rods is approximately normally distributed, with a standard deviation of 0.07 cm. How long does a rod need to be to fall in the shortest 10% rods?

24.91 cm or less

A researcher wants a margin of error of 2.4 for a 90% CI estimate and he wonders what sample size he should consider. He knows that the population of his interest follows a normal distribution with known standard deviation σ = 7.25 . What sample size should you recommend for a 90% CI of μ ?

25

For a 95% confidence interval estimate for the mean μ , what is the margin of error of the estimation for a sample of size 36? It is known that the population standard deviation σ = 9.5 .

3.103

In a sample of 123 hip surgeries of certain type, the average surgery time was 136.9 minutes with a standard deviation of 22.6 minutes. What would be the length of the 90% confidence interval constructed here?

6.76 minutes

The time to complete a standardized exam is approximately Normal with a mean of 1 hour 10 minutes and a standard deviation of 10 minutes. How much time should be given to complete the exam so 80% of the students will complete the exam in the time given?

78.4 minutes

The weight of male babies less than 2 months old in the United States is normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds. What is the first quartile of the baby weight distribution?

9.679

The data below refers to the time in hours spent on mobile internet by sample of 10 students in a class. 39 42 47 45 32 45 37 34 33 29 Assume that the population data follows a normal distribution with unknown mean and unknown standard deviation. For a 95% confidence interval estimate of μ , what confidence interval method will you use?

T Confidence Interval

To estimate the average age of all diabetic people in the population, a 90% and 95% confidence intervals are constructed based on the same sample of size n. Assume that the population standard deviation is known. The 95% confidence interval will be wider than the 90% confidence interval. Is this a true statement?

Yes

A sample of 314 patients between the ages of 38 and 82 were given a combination of the drugs ezetimibe and simvastatin. They achieved a mean reduction in total cholesterol of 0.94 milimole per liter. Assume the population standard deviation is σ = 0.18. Construct a 95% confidence interval for the mean reduction in total cholesterol in patients who take this combination of drugs.

[0.92, 0.96] milimole per liter

A social scientist wishes to estimate the mean number of years of education μ for adults in a certain large city. She surveys a random sample of 100 adults and find that the sample mean is 12.98 years and sample variance of is 9. Construct a 99% confidence interval for the mean number of years of education for adults in the city.

[12.192, 13.768] years

The average salary of doctors is unknown to a researcher. The researcher knows that the salary is normally distributed with population standard deviation 30. To estimate the average salary, the researcher takes a sample of 25 doctors whose average (mean) salary is found to be 152 thousand dollars/year. Find a 90% CI estimate of the average salary μ of all doctors.

[142.13, 161.87] thousand dollars

The data below refers to the time in hours spent on mobile internet by sample of 10 students in a class. 39 42 47 45 32 45 37 34 33 29 Assume that the population data follows a normal distribution with unknown mean and unknown standard deviation. Find a 95% confidence interval estimate of μ .

[33.813, 42.787] hours

Data below refers to the waiting time in minutes for a sample of 10 customers for an oil change at a certain oil change station. It follows that the time for an oil change for the station follows a normal distribution with population standard deviation σ = 7.5 minutes. 38 42 47 45 35 45 37 34 33 41 Find a 90% CI of unknown mean time μ for an oil change. [The answer choices are provided in minutes.]

[35.8, 43.6]

The Pew Internet and American Life Project surveyed 2227 adults, asking them about their texting habits. Among men, the mean number of text messages sent per day was 40.9, and among women it was 42.0. Assume that 1085 men and 1142 women were sampled, and that the sample standard deviations were 56.5 for the men and 51.4 for the women. Assume that the samples are coming from approximately normal distributions. Construct 95% confidence intervals for mean number of texts for men group.

[37.534, 44.266]

The Pew Internet and American Life Project surveyed 2227 adults, asking them about their texting habits. Among men, the mean number of text messages sent per day was 40.9, and among women it was 42.0. Assume that 1085 men and 1142 women were sampled, and that the sample standard deviations were 56.5 for the men and 51.4 for the women. Assume that the samples are coming from approximately normal distributions. Construct 95% confidence intervals for mean number of texts for women group.

[39.016, 44.984]

The location parameter of a normal distribution is

its mean