代做ECON 83a: Statistics for Economic Analysis Problem Set #4, Spring 2021代写数据结构语言程序

ECON 83a: Statistics for Economic Analysis

Problem Set #4, Spring 2021

1. The driving time for an individual from her home to her work is uniformly dis-tributed between 300 to 480 seconds.

a. Determine the probability density function.

b. Compute the probability that the driving time will be less than or equal to 435 seconds.

c. Determine the expected driving time.

d. Compute the variance.

e. Compute the standard deviation.

2. The length of time patients must wait to see a doctor in a local clinic is uniformly distributed between 15 minutes and 2.5 hours.

a. What is the probability of a patient waiting exactly 50 minutes?

b. What is the probability that a patient would have to wait between 45 minutes and 2 hours?

c. Compute the probability that a patient would have to wait over 2 hours.

d. Determine the expected waiting time and its standard deviation.

3. z is a standard normal random variable. Compute the following probabilities.

a. P(-1.23 < z < 2.58)

b. P(1.83 < z < 1.96)

c. P(z > 1.32)

d. P(z < 2.52)

e. P(z > -1.63)

f. P(z < -1.38)

g. P(-2.37 < z < -1.54)

h. P(z = 2.56)

4. z is a standard normal random variable. Find the value of z in the following.

a. The area between 0 and z is 0.4678.

b. The area to the right of z is 0.1112.

c. The area to the left of z is 0.8554

d. The area between -z and z is 0.754.

e. The area to the left of -z is 0.0681.

f. The area to the right of -z is 0.9803.

5. “DRUGS R US” is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a standard deviation of 0.3 ounces. Assume the contents of the bottles are normally distributed.

a. What percentage of all bottles produced contains more than 6.51 ounces of vita- mins?

b. What percentage of all bottles produced contains less than 5.415 ounces?

c. What percentage of bottles produced contains between 5.46 to 6.495 ounces?

d. Ninety-five percent of the bottles will contain at least how many ounces?

e. What percentage of the bottles contains between 6.3 and 6.6 ounces?

6. The Globe Fishery packs shrimp that weigh more than 1.91 ounces each in pack- ages marked “large” and shrimp that weigh less than 0.47 ounces each into pack- ages marked “small”; the remainder are packed in “medium” size packages.  If a day’s catch showed that 19.77 percent of the shrimp were large and 6.06 per- cent were small, determine the mean and the standard deviation for the shrimp weights. Assume that the shrimps’ weights are normally distributed.

7. The monthly income of residents of Daisy City is normally distributed with a mean of $3,000 and a standard deviation of $500.

a. The mayor of Daisy City makes $2,250 a month. What percentage of Daisy City’s residents has incomes that are more than the mayor’s?

b. Individuals withincomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes?

c. What are the minimum and the maximum incomes of the middle 95% of the residents?

d. Two hundred residents have incomes of at least $4,440 per month. What is the population of Daisy City?

8. x is a normal random variable. It is known that for 27.34% of all the items 100 < x < m, i.e. these items have values of x that are between 100 and the expected value of this normal distribution. For another 45.99% of all the items m < x < 145, i.e. these items have values of x that are between the expected value of this normal distribution and 145. Determine the expected value and the standard deviation of the distribution.