A uniform distribution is defined over the interval from 6 to 10.
a. What is the value of a and b?
b. What is the mean of this uniform distribution?
c. What is the standard deviation?
d. Show that the probability of any value between 6 and 10 is equal to 1.0
e. What is the probability that the random variable is more than7?
f. What is the probability that the random variable is between 7 and 9?
g. What is the probability that a random variable is equal to 6.52?
2. According to the insurance Institute of America, a family of four spends between $400
and $3800 per year on all types of insurance. Suppose the money spent is uniformly
distributed between these amounts.
a. What is the mean amount spent on insurance?
b. What is the standard deviation of the amount spent?
c. If we select a family at random, what is the probability they spend less than $2000
per year on insurance?
d. What is the probability a family spends more than $3000 per year on insurance?
3. The mean of a normal probability distribution is 500, the standard deviation is 10.
a. About 68% of the observations lie between what two values?
b. About 95% of the observations lie between what two values?
a. About what percent of the observations lie between 470 and 530?
4. The mean salary of workers of a company is $25,000 with a standard deviation of $250.
Calculate the z-score for John’s salary of $24,800
5. The internal revenue service reported that the average refund in 2017 was $2,878 with a
standard deviation of $520. Assume the amount refunded is normally distributed.
a. What percent of the refunds are more than $3,500?
b. What percent of the refunds are between $3,500 and $4,000?
c. What percent of the refunds are less than $2,950?