1) Let   x be a continuous random variable thatfollows a normal distribution with a mean of 321 and a standarddeviation of 41.

(a) Find the value of   x > 321 sothat the area under the normal curve from 321 to x is 0.2224.

Round your answer to the nearest integer.
The value of   x is_______

(b) Find the value of x so that the area underthe normal curve to the right of x is 0.3745.

Round your answer to the nearest integer.
The value of   x is ______

2) A study has shown that 24% of all college textbooks have aprice of $80 or higher. It is known that the standard deviation ofthe prices of all college textbooks is $10.00. Suppose the pricesof all college textbooks have a normal distribution. What is themean price of all college textbooks?

Round your answer to the nearest integer.

μ=

3) Use a table, calculator, or computer to find the specifiedarea under a standard normal curve.

Round your answers to 4 decimal places.

a) More than a z-score of 2.48; area =_____________

b) More than a z-score of 1.7; area =_____________

c) More than a z-score of -0.41; area =_____________

d) More than a z-score of 00; area = _____________

4)

The highway police in a certain state are using aerialsurveillance to control speeding on a highway with a posted speedlimit of 55 miles per hour. Police officers watch cars fromhelicopters above a straight segment of this highway that has largemarks painted on the pavement at  1-mile intervals. Afterthe police officers observe how long a car takes to cover the mile,a computer estimates that cars speed. Assume that the errors ofthese estimates are normally distributed with a meanof  0 and a standard deviation of  3.58 milesper hour.

a. The state police chief has directed hisofficers not to issue a speeding citation unless the aerial unitsestimate of speed is at least 66 miles per hour. What is theprobability that a car travelling at 61 miles per hour or slowerwill be cited for speeding?

Round your answer to four decimal places.

The probability that a car travelling at 61 miles per hour orslower will be cited for speeding is ______

b. Suppose the chief does not want his officersto cite a car for speeding unless they are 99% sure that it istravelling at 61 miles per hour or faster. What is the minimumestimate of speed at which a car should be cited for speeding?

Round your answer to the nearest integer.

The minimum estimate of speed is __