# Statistics Problems: Mean, probability, standard deviation, confidence interval

1. You are a manager of a Starbucks located at Southcenter Mall. Recently, a new local coffee shop specializing in lattes has opened in the Mall. You are wondering what the impact on your latte sales may be. You know from previous data tracking that the largest number of lattes sold at your location is during the morning. Thus, you decide to pull data from the last 2 weeks on the number of lattes sold between 7:00 - 10:00 am on weekdays. The raw data is as follows:

65 70 53 57 81 79 77 68 88 85

a) Find the arithmetic mean and the standard deviation of lattes sold from 7:00-10:00am. Discuss the meaning of these numbers within the context of the problem.

b) Are the values in part (a) called statistics or parameters? Why?

2. A quality control procedure for testing Ready-Flash flash bulbs consists of drawing two bulbs at random from each lot of 100. If both are defective, the entire lot is rejected. Find the probability that both bulbs are defective if the lot contains 10 defective flash bulbs. Since we are drawing bulbs at random, assume each bulb in the lot has an equal chance of being drawn.

a) What is the probability of getting a defective bulb on the first draw?

b) If the first bulb drawn is not replaced, what is the probability of getting a defective bulb on the second draw if the first bulb was defective?

c) Are the probabilities computed in parts a and b different? Does drawing a defective bulb on the first draw change the probability of getting a defective bulb on the second draw? Are the events dependent or independent?

d) Compute: P(1st bulb defective and 2nd bulb defective).

3. The American Restaurant Association collected information on the number of meals eaten outside the home per week by young married couples. A survey of 60 couples showed the sample mean number of meals eaten outside the home was 2.76 meals per week, with a standard deviation of .75 meals per week.

a) Construct a 95% confidence interval for the population mean.

b) How would the interval change if you lowered the confidence level from 95% to 90%?

4. The First National Bank of Wilson has 650 checking account customers. A recent sample of 50 of these customers showed 26 to have a Visa card with the bank. Construct the 99 percent confidence interval for the proportion of checking account customers who have a Visa card with the bank.

5. The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of visitors who plan to camp in the state. Current estimates are that 35 percent of visitors are campers. How large a sample would you take to estimate at a 95 percent confidence level the population proportion with an allowable error of 2 percent?

6. The Myers Summer Casual Furniture Store tells customers that a special order will take six weeks (42 days). During recent months the owner has received several complaints that the special orders are taking longer than 42 days. A sample of 12 special orders delivered in the last month showed that the mean waiting time was 51 days with a standard deviation of 8 days. At the .05 significance level, are customers waiting an average of more than 42 days?

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#### Solution Summary

Step by step method for computing Mean, probability, standard deviation, confidence interval and test statistic is given in the answer.

Probability, Test Statistics and Error

In a recent year, scores on a standardized test for high schools student with a 3.50 to 4.00 grade point average were normally distributed, with a mean of 37.9 and a standard deviation of 2.4. A student with a 3.50 to 4.00 grade point average who took the standardized test is randomly selected.

Four Decimal Places for Questions

Find the probability of a student test score less than 36

The probability of a student scoring less than 36 is ________

Find the probability of a student test score between 35.1 and 40.7

The probability of a student scoring between 35.1 and 40.7 is ________

Find the probability of a student test score more than 39.3

The probability of a student scoring more than 39.3 is ___________

_________________________________

*A microwave oven repairer says that the mean repair cost for damaged microwave ovens is less than $110. You work for the repairer and want to test this claim. You find that a random sample of five microwave ovens has a mean repair cost of $115 and a standard deviation of $12.50. At a=0.05, do you have enough to support the repairer's claim? Assume the population is normally distributed.

What is (are) the critical value(s), t0? t0 = _________

Find the standardized test statistic t = __________

*Use the confidence interval to find the estimated margin of error. Then find the sample mean. A biologist reports a confidence interval of (2,9,4,5) when estimating the mean height (in centimeters) of a sample seedlings.

A. The estimated margin of error is _______

B. The Sample mean is ________

_____________________________________________

*Construct the 95% and 99% confidence intervals for the population proportion "p" using the sample statistics below. Which interval is wider? If convenient, use technology to construct the confidence intervals.

Three decimal places as needed

95% confidence intervals for the population proportion "p" is _____ - ______

99% confidence intervals for the population proportion "p" is _____ - ______

Which interval is wider? 95% confidence intervals or 99% confidence intervals

__________________________________________

*Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p: n=80, p=0.5

The mean, u, is __________ (nearest tenth)

Variance, 2 is_______ (nearest tenth)

The standard deviation, , is ________ (nearest tenth)

______________________________________________

*A frequency distribution is shown below. Complete part (a) through (e)

The number of dogs per household in a small town

Dog 0 1 2 3 4 5

Household 1370 406 163 50 26 16

0 ___ 1___2___3___4___5___ (nearest thousand)

Find the mean of the probability distribution: u=______ (nearest tenth)

Find the variance of the probability distribution: 2 = ________(nearest tenth)

Find the standard deviation of the probability distribution: = ___(nearest tenth)