Problem 1: The ages of a group of 50 women are approximately normally distributed with a mean of 49 years and a standard deviation of 6 years. One woman is randomly selected from the group, and her age is observed.
a. Find the probability that her age will fall between 54 and 60 years.
b. Find the probability that her age will fall between 47 and 52 years.
c. Find the probability that her age will be less than 34 years.
d. Find the probability that her age will exceed 40 years.
Problem 2: The mean gas mileage for a hybrid car is 57 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.5 miles per gallon.
a. What is the probability that a randomly selected hybrid gets more than 62 miles per gallon?
b. What is the probability that a randomly selected hybrid gets 50 miles per gallon or less?
c. What is the probability that a randomly selected hybrid gets between 59 and 62 miles per gallon?
d. What is the probability that a randomly selected hybrid gets less than 45 miles per gallon?
Problem 3: Resource Reservation Protocol (RSVP) was originally designed to establish signaling links for stationary networks. RSVP was applied to mobile wireless technology. A simulation study revealed that the transmission delay (measured in milliseconds) of an RSVP linked wireless device has an approximate normal distribution with mean g = 46.5 milliseconds and a = 8.5 milliseconds. Complete carts a and b.
a. What is the probability that the transmission delay is less than 57 milliseconds?
Attachment:- Doc2hw.docx