# Normal Probability

1. The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45.

a. What is the probability that a randomly selected teacher earns more than $525 per week?

b. What is the probability a randomly selected teacher earns less than $435 per week?

2. The introductory salaries for medical billing clerks are normally distributed with a mean of $24,800 and a standard deviation of $2850.

a. What percent of introductory salaries are less than $23,000?

b. What percent of introductory salaries are between $21,250 and $23,750?

3. The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 109 inches, and a standard deviation of 10 inches.

a. What is the probability that the mean annual snowfall during 40 randomly picked years will exceed 111.8 inches?

b. What is the probability that the mean annual snowfall during 40 randomly picked years will be between 105 inches and 112 inches?

4. Merta claims that 74% of its trains are on time.

a. Find the probability that among the 60 trains, 38 or fewer arrived on time.

b. Find the probability that among the 60 trains, 50 or more arrived on time.

For problems 1 through 8 you will be asked to determine the following probabilities using tables from https://netfiles.uiuc.edu/dunger/stat200/Normal%20Tables.pdf.

1. P(z<-1.53)

2. P(z>2.61)

3. P(-1.62 < z < 2.81)

4. P P(2.15 < z < 2.94)

5. The z-score that would create a right tail of 31%.

6. The z-score that would create a left tail of 6.5%.

7. P(x > 74) in a normally distributed set of data with a mean of 62 and a standard deviation of 9.

8. P(49 < x < 78) in a normally distributed set of data with a mean of 62 and a standard deviation of 9.

9. The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 109 inches, and a standard deviation of 10 inches. If 40 snowfall amounts are randomly selected, find x-bar for the sampling distribution of sample means with samples of size 40.

10. The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 109 inches, and a standard deviation of 10 inches. If 40 snowfall amounts are randomly selected, find x-bar for the sampling distribution of sample means with samples of size 40.

#### Solution Summary

The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included.