# Standard Deviation and Probability

1) Hourly wages at the amusement park are normally distributed with a mean of $8.55 per hour and a standard deviation of $0.45. If an employee is selected at random, what is the probability that the worker earns less than $7.75 per hour?

2) The number of years at a bank is normally distributed with a mean of 10.5 years and a standard deviation of 4.6 years. If an employee is selected at random, what is the probability that the employee has worked for the company for more than 9 years?

3) The price of breakfast is normally distributed with a mean of $5.85 and a standard deviation of $0.35. If a meal is selected at random, what is the probability that its price is between $5.90 and $6.10?

4) A school accepts the top 10% of the applicants based on the entrance exam. The scores are normally distributed with a mean of 88 and a standard deviation of 3. What is the cutoff score to be admitted to the school?

5) The price of tickets at a theater is normally distributed with a mean of $75 and a standard deviation of $5.25. What are the minimum and maximum prices in the middle 75% range?

6) A study shows that the mean number of hours children watch television each day is 4 hours with a standard deviation of 1.8 hours. If the number of hours is normally distributed, what is the probability that the mean time spent by a randomly selected group of 81 children watching TV each day is under 5.5 hours?

Feel free to use this website to help you compute your answers:

www.davidmlane.com/hyperstat/z_table.html.

Â© BrainMass Inc. brainmass.com March 4, 2021, 7:53 pm ad1c9bdddfhttps://brainmass.com/math/probability/standard-deviation-normal-distributions-z-scores-probability-129997

#### Solution Summary

Standard deviation and probability are investigated in the solution.