Question: 1- Given that z is a standard Normal random variable, find following probabilities: a. P(z <0.68) b. P(z> -0.21) c. P(-0.42 11.5) c. P(8.9

Question:1- Given that z is astandardNormal random variable, find following probabilities:

a. P(z<0.68)

b.P(z> -0.21)

c. P(-0.42

2- Given that z is astandardNormal random variable, find z for each situation: the area to the left of z is 0.57

a. the area to the right of z is 0.84

b.the total area to the left of -z and to the right of z is 0.5

3- Given that x is a Normal random variable with a mean of 10 and standard deviation of 4, find following probabilities:

a. P(x<7.6)

b. P(x>11.5)

c. P(8.9

4- Given that x is a Normal random variable with a mean of 10 and standard deviation of 4, find x for each situation:

a. the area to the left of x is 0.1

b. the area to the left of x is 0.75

c. the area to the right of x is 0.35

d. the area to the right of x is 0.95

5- the length of incoming calls at the call center of a major telecommunication service provider follows a Normal distribution with an average of 7.5 minutes. If the standard deviation of the distribution is 5 minutes.

a. What is the probability that the length of an incoming call is longer than 9.5 minutes?

b. What is the probability that the length of an incoming call is shorter than 6 minutes?

c. What is the probability that the length of an incoming call is between 6.5 to 25 minutes?

d. 25% of the incoming calls is longer than how many minutes?

6- the servicing time at the drive-through lane of a fast food restaurant follows an exponential distribution. The average servicing time is 1.5 minutes.

a. What is the probability that it takes more than 2 minutes to service a customer at the drive-through lane?

b. What percent of customers at the drive-through lane will take between 1 to 2 minutes to service?