1. Suppose that the speed at which cars go on the freeway is normally distributed with mean 69 mph and standard deviation 8 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. If one car is randomly chosen, find the probability that it is traveling more than 68 mph.
c. If one of the cars is randomly chosen, find the probability that it is traveling between 72 and 76 mph.
2. In the 1992 presidential election, Alaska’s 40 election districts averaged 1803 votes per district for President Clinton. The standard deviation was 552. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts) Round all answers except part e. to 4 decimal places.
a. What is the distribution of X? X ~ N(,)
b. Is 1803 a population mean or a sample mean?
c. Find the probability that a randomly selected district had fewer than 1657 votes for President Clinton.
d. Find the probability that a randomly selected district had between 1983 and 2184 votes for President Clinton.
e. Find the third quartile for votes for President Clinton. Round your answer to the nearest whole number.
3. Suppose that the weight of seedless watermelons is normally distributed with mean 6.9 kg. and standard deviation 1.5 kg. Let X be the weight of a randomly selected seedless watermelon. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. What is the median seedless watermelon weight? kg.
c. What is the Z-score for a seedless watermelon weighing 8.3 kg?
d. What is the probability that a randomly selected watermelon will weigh more than 7.5 kg?
e. What is the probability that a randomly selected seedless watermelon will weigh between 7.2 and 7.8 kg?
f. The 90th percentile for the weight of seedless watermelons is kg.
4. On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 102 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual.
a. What is the distribution of X? X ~ N(,)
b. Find the probability that a randomly selected person’s IQ is over 112. Round your answer to 4 decimal places.
