Work needs to be shown for all problems. If this is completed, you will be my hero.
1. A random variable X is normally distributed with a mean of 37 and a standard deviation of 10.
a. What is the probability that X will be more than 50?
b. What is the probability that X will be more than 30?
c. What is the probability that X will be more than 25 but less than 55?
d. What is the probability that X will be more than 45 but less than 65?
e. What is the value of x such that 37% of the X values are less than x?
2. The number of phone calls each hour at a customer call center is normally distributed with an average of 54 and a standard deviation of 11.
a. What is the probability that there will be less than 47 calls in an hour?
b. What is the probability that there will be less than 72 calls in an hour?
c. What is the probability that there will be between 45 and 50 calls in an hour?
d. What is the number of calls such that you can be 94% sure there will be no more
than that number of calls in an hour?
e. What are the two numbers of calls, one on each side of the average and equally
distant from the average, such that you can be 98% sure that the number of calls in an
hour will fall between those two numbers of calls?