Exam 10: Probability and Calculus

The function f is a probability density function defined on the given interval. Find . ​ ​

Let Z be the standard normal variable. Find the value of z if z satisfies . Round your answer to the nearest hundredth. ​

The amount of time t (in minutes) a shopper spends browsing in the magazine section of a supermarket is a continuous random variable with probability density function ​ ​ How much time is a shopper chosen at random expected to spend in the magazine section?

The amount of time t (in minutes) a shopper spends browsing in the magazine section of a supermarket is a continuous random variable with probability density function ​ ​ ​ How much time is a shopper chosen at random expected to spend in the magazine section? ​

A study conducted by Uni-Mart, a mail-order department store, reveals that the time intervals in minutes between incoming telephone calls on its toll-free 600 line between 9 A.M. and 2 P.M. are exponentially distributed with probability density function . What is the probability that the time interval between successive calls is more than 6 min? Round your answer to four decimal places. ​

Find the median of the random variable x with the probability density function defined on the indicated interval I. The median of x is defined to be the number m such that . Observe that half of the x-values lie below m and the other half lie above m. ​ ​ __________

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. Round your answer to four decimal places. ​ ​ ​

Let Z be the standard normal variable. Find the values of z if z satisfies . Round your answer to the nearest hundredth. ​