Given that z is a standard normal random variable, find z for each situation.

The area to the left of z is .2119.

Given that $z$ is a standard normal random variable, compute the following probabilities.

$$P ( - 1.98 \leq z \leq .49 )$$

Given that $z$ is a standard normal random variable, compute the following probabilities.

$$P ( 0 \leq z \leq 83 )$$

Given that z is a standard normal random variable, find z for each situation.

The area between -z and z is .2052.

Given that z is a standard normal random variable, find z for each situation.

The area to the right of z is .6915.

Given that z is a standard normal random variable, find z for each situation.

The area between -z and z is .9030.

Given that z is a standard normal random variable, find z for each situation.

The area to the left of z is .7291.

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions.

What is the probability of completing the exam in one hour or less?

The average return for large-cap domestic stock funds over the three years 2009-2011 was $14.4\%$ (AA/I Journal, February 2012). Assume the three-year returns were normally distributed across funds with a standard deviation of $4.4\%$. a. What is the probability an individual large-cap domestic stock fund had a three-year return of at least $20\%$?

Given that z is a standard normal random variable, find z for each situation.

The area to the left of z is .9948.

Given that z is a standard normal random variable, find z for each situation.

The area to the right of z is .3300.

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces. Calculate the probability of a defect and the expected number of defects for a 1000-unit production run in the following situations.

The process standard deviation is .15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects.

Given that z is a standard normal random variable, find z for each situation.

The area to the left of z is .6700.

Automobile Repair Costs. Automobile repair costs continue to rise with the average cost now at $\$ 367$ per repair (U.S. News & World Report website). Assume that the cost for an automobile repair is normally distributed with a standard deviation of $\$ 88$. Answer the following questions about the cost of automobile repairs.

d. If the cost for your car repair is in the lower $5 \%$ of automobile repair charges, what is your cost?