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

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?