Question

1. The amount of money spent by a customer at a discount store has a mean of $100 and a standard deviation of $30. What is the probability that a randomly selected group of 50 shoppers will spend a total of more than $5700? (Hint: The total will be more than $5700 when the sample average exceeds what value?) (Round the answer to four decimal places.)
P(total > 5700) =  

2. Five students visiting the student health center for a free dental examination during National Dental Hygiene Month were asked how many months had passed since their last visit to a dentist. Their responses were as follows.

7

15

10

22

28

Assuming that these five students can be considered a random sample of all students participating in the free checkup program, construct a 95% confidence interval for the mean number of months elapsed since the last visit to a dentist for the population of students participating in the program. (Give the answer to two decimal places.)

3.

In a study investigating the effect of car speed on accident severity, 5,000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5,000 accidents, the average speed was 47 mph and the standard deviation was 16 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal. (Use the Empirical Rule.)

(a)

Approximately what percentage of vehicle speeds were between 31 and 63 mph?

approximately  %

(b)

Approximately what percentage of vehicle speeds exceeded 63 mph? (Round your answer to the nearest whole number.)

approximately  %

4.

The average reading speed of students completing a speed-reading course is 400 words per minute (wpm). If the standard deviation is 40 wpm, find the z score associated with each of the following reading speeds. (Round the answers to two decimal places.)

270 wpm
425 wpm
350 wpm
520 wpm

Answer 1

1.

The probability is obtained from the z distribution table. In excel use function =1-NORM.S.DIST(3.2998,TRUE)

2.

The confidence interval for the mean is obtained using the formula,

From the data values,

The t critical value is obtained from t distribution table for significance level = 0.05 and degree of freedom = n -1 = 5 - 1 = 4.

3.

(a)

Using the empirical rule approximately 68.27% of vehicle speeds lie within one standard deviation from the mean

(b)

approximately 16 %

4.

For 270 wpm

For 425 wpm

For 350 wpm

For 520 wpm