1. Find the following probability for the standard normal random variable z P(-2.5 z 2.5) 2. Suppose x is a normal distributed random variable with = 15 and = 2. Find each of the following probabilities. a. P(x18.5) b. P(x11) c. P(16.56x19.58) d. P(9.52x18.6) 3. The ages of a group of 50 women are approximately normally distributed with a mean of 50 years and a standard deviation of 5 years. One woman is randomly selected from the group, and her age is observed. a. Find the probability that her age will fall between 55 and 60 years. b. Find the probability that her age will fall between 49 and 53 years. c. Find the probability that her age will be less than 34 years. d. Find the probability that her age will exceed 41 years 4.Financial analysts who make forecasts of stock prices are categorized as either \"buy-side\" analysts or \"sell-side\" analysts. The mean and standard deviation of the forecast errors for both types of analysts are shown is the table to the right. Assume that the distribution of forecast errors are approximately normally distributed. Mean Standard deviation Buy-side analysts .82 1.94 Sell-side analysts -.03 .86 a. Find the probability that a buy-side analyst has a forecast error of + 2.02 or higher b. Find the probability that a sell-side analyst has a forecast error of + 2.02 or higher 4. The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.2 miles per gallon. a. What is the probability that a randomly selected hybrid gets more than 60 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 58 and 61 miles per gallon? d. What is the probability that a randomly selected hybrid gets less than 45 miles per gallon? 5. 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 =49.5 milliseconds and = 8.5 milliseconds. Complete part a and b. a. what is the probability that the transmission delay is less that 57 milliseconds? P(X<57)=? B. What is the probability that the transmission delay is between 40 and 60 milliseconds