This assignment is required to be submitted, both the non-text book problems and the textbook problems.
Part One Text Book Problems:
Chapter Seven Work: p. 235: 7.2; p. 236: 7.9; p. 238: 7.13; p. 241: 7.26, 7.27
Part Two Non-text Book Problems:
1. When considering Excel functions, describe the difference between =NORMSDIST(z) and =NORMDIST(z, μ , σ , 1)
2. Since 1894 Hershey’s milk chocolate bars have been manufactured in Hershey, PA. A random sample of 100 chocolate bars was taken and weighed. The mean weight was found to be 80 grams with a standard deviation of 20 grams. What weight in grams would 95% of all possible sample means fall above?
3. In accordance with the requirements of the National Traffic and Motor Vehicle safety Act, if you own a Lexus manufactured between 2002 and 2017, your vehicle may be subject to a safety recall for your passenger side airbag. Generally the time involved for the recall appointments is normally distributed with a mean of 45 minutes and a standard deviation of 11 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean is between 45 and 50 minutes?
Multiple Choice: Please include why you choose the answer for the multiple choice questions.
4. Regarding the sampling distribution of the mean for a large sample size Which of the following is true?
a. It has the same shape, mean, and standard deviation as the population.
b. It has a normal distribution with the same mean and standard deviation as the population.
c. It has the same shape and mean as the population but has a smaller standard deviation.
d. It has a normal distribution with the same mean as the population but with a smaller standard deviation.
5. The standard error of the population proportion will become larger
a. as population proportion approaches 0.
b. as population proportion approaches 0.50.
c. as population proportion approaches 1.00.
d. as the sample size increases.
7.2 Given a normal distribution with μ=50 and σ=5,
if you select a sample of n=100,what is the probability that
a. less than 47?
b. between 47 and 49.5?
c. above 51.1?
d. There is a 35% chance that X is above what value?
7.9 According to a report by App Annie, a business intelligence company that produces tools and reports for the apps and digital goods industry, smartphone owners are using an average of 30 apps per month.
Source: “Report: Smartphone owners are using 9 apps per day, 30 per month,” 2017, tcrn.ch/2qK4iRr.
Assume that number of apps used per month by smartphone owners is normally distributed and that the standard deviation is 5. If you select a random sample of 25 smartphone owners,
a. what is the probability that the sample mean is between 29 and 31?
b. what is the probability that the sample mean is between 28 and 32?
c. If you select a random sample of 100 smartphone owners, what is the probability that the sample mean is between 29 and 31?
d. Explain the difference in the results of (a) and (c).
7.13 The following data represent the yes or no (Y or N) responses from a sample of 40 college students to the question “Do you currently own shares in any stocks?”
a. Determine the sample proportion, p, of college students who own shares of stock.
b. If the population proportion is 0.30, determine the standard error of the proportion.
7.26 An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearing can operate are 0.74 inch (lower) and 0.76 inch (upper). Past experience has indicated that the actual diameter of the ball bearings is approximately normally distributed, with a mean of 0.753 inch and a standard deviation of 0.004 inch. If you select a random sample of 25 ball bearings, what is the probability that the sample mean is
a. between the target and the population mean of 0.753?
b. between the lower specification limit and the target?
c. greater than the upper specification limit?
d. less than the lower specification limit?
e. The probability is 93% that the sample mean diameter will be greater than what value?
7.27 The fill amount of bottles of a soft drink is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If you select a random sample of 25 bottles, what is the probability that the sample mean will be
a. between 1.99 and 2.0 liters?
b. below 1.98 liters?
c. greater than 2.01 liters?
d. The probability is 99% that the sample mean amount of soft drink will be at least how much?
e. The probability is 99% that the sample mean amount of soft drink will be between which two values (symmetrically distributed around the mean)?