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1. The average licensed driver...

1. The average licensed driver travels 1,536 miles per month in his or her vehicle. Assume the population standard deviation is 429 miles per month. Determine the interval that will contain 96% of the sample means for the sample sizes in parts a through c.

a. 30 drivers

b. 40 drivers

c. 50 drivers

d. Explain the differences in these probabilities.

a. Using a sample size of 30 the lower bound of the symmetrical interval is nothing and the upper bound is nothing.

(Type an integer or decimal rounded to one decimal place as needed.)

b. Using a sample size of 40 the lower bound of the symmetrical interval is nothing and the upper bound is nothing.

(Type an integer or decimal rounded to one decimal place as needed.)

c. Using a sample size of 50 the lower bound of the symmetrical interval is nothing and the upper bound is nothing.

(Type an integer or decimal rounded to one decimal place as needed.)

d. Increasing the sample size

▼

does not affect

reduces

increases

the standard error. This, in turn,

▼

increases

reduces

the probabilities that the sample mean will be closer to the population mean.

2. A cell phone company would like to estimate the average number of text messages received by American teenagers per month. A random sample of 58 teenaged customers was selected. The sample average was 2,276 messages per month, and the sample standard deviation was 940 messages per month. Construct confidence intervals with the given confidence levels.

a.

90%

b.

95%

c.

99%

a. The 90% confidence interval has a lower limit of nothing and an upper limit of nothing.

(Type integers or decimals rounded to one decimal place as needed.)

b. The 95% confidence interval has a lower limit of nothing and an upper limit of nothing.

(Type integers or decimals rounded to one decimal place as needed.)

c. The 99% confidence interval has a lower limit of nothing and an upper limit of nothing.

(Type integers or decimals rounded to one decimal place as needed.)

3. According to a national agency, the average cost of care for an infant in a child-care center in a particular state was $8,814 per year. Assume this cost follows a normal distribution with a standard deviation of $975.

a. What is the probability that a randomly selected child-care center in the state costs

1. more than $8,000 per year for infant care?

2. more than $9,000 per year for infant care?

3. between $8,500 and $9,500 per year for infant care?

b. Determine the rate a child-care center that wishes to be in the 80th percentile in the state should charge for an infant.

a. 1. The probability is nothing.

(Round to four decimal places as needed.)

a. 2. The probability is nothing.

(Round to four decimal places as needed.)

a. 3. The probability is nothing.

(Round to four decimal places as needed.)

b. The child-care center should charge $nothing.

(Round to the nearest dollar as needed.)

a. 30 drivers

b. 40 drivers

c. 50 drivers

d. Explain the differences in these probabilities.

a. Using a sample size of 30 the lower bound of the symmetrical interval is nothing and the upper bound is nothing.

(Type an integer or decimal rounded to one decimal place as needed.)

b. Using a sample size of 40 the lower bound of the symmetrical interval is nothing and the upper bound is nothing.

(Type an integer or decimal rounded to one decimal place as needed.)

c. Using a sample size of 50 the lower bound of the symmetrical interval is nothing and the upper bound is nothing.

(Type an integer or decimal rounded to one decimal place as needed.)

d. Increasing the sample size

▼

does not affect

reduces

increases

the standard error. This, in turn,

▼

increases

reduces

the probabilities that the sample mean will be closer to the population mean.

2. A cell phone company would like to estimate the average number of text messages received by American teenagers per month. A random sample of 58 teenaged customers was selected. The sample average was 2,276 messages per month, and the sample standard deviation was 940 messages per month. Construct confidence intervals with the given confidence levels.

a.

90%

b.

95%

c.

99%

a. The 90% confidence interval has a lower limit of nothing and an upper limit of nothing.

(Type integers or decimals rounded to one decimal place as needed.)

b. The 95% confidence interval has a lower limit of nothing and an upper limit of nothing.

(Type integers or decimals rounded to one decimal place as needed.)

c. The 99% confidence interval has a lower limit of nothing and an upper limit of nothing.

(Type integers or decimals rounded to one decimal place as needed.)

3. According to a national agency, the average cost of care for an infant in a child-care center in a particular state was $8,814 per year. Assume this cost follows a normal distribution with a standard deviation of $975.

a. What is the probability that a randomly selected child-care center in the state costs

1. more than $8,000 per year for infant care?

2. more than $9,000 per year for infant care?

3. between $8,500 and $9,500 per year for infant care?

b. Determine the rate a child-care center that wishes to be in the 80th percentile in the state should charge for an infant.

a. 1. The probability is nothing.

(Round to four decimal places as needed.)

a. 2. The probability is nothing.

(Round to four decimal places as needed.)

a. 3. The probability is nothing.

(Round to four decimal places as needed.)

b. The child-care center should charge $nothing.

(Round to the nearest dollar as needed.)

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