Statistics and Probability Answers

5) It is known that amounts of money spent on clothing in a year by students on a particular campus follow a normal distribution with a mean of $380 and a standard deviation of $50. a. What is the probability that a randomly chosen student will spend less than $400 on clothing in a year? b. What is the probability that a randomly chosen student will spend more than $360 on clothing in a year? c. What is the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year?

Probability Distribution Problem

1.) I throw a die and get P1.00 if it is showing 1, get P2.00 if it is showing 2, P3.00 if it

is showing 3, P4.00 if it is showing 4, P5.00 if it is showing 5, and get P6.00 if it is

showing 6. What is the amount of money I can expect if I throw it 100 times?

complete solution

3) MRP produces lightbulbs whose life follows a normal distribution, with a mean of 1,200 hours and a standard deviation of 250 hours.  a. If we choose a lightbulb at random, what is the probability that its lifetime will be between 900 and 1,300 hours? b. If we choose a lightbulb at random, what is the probability that its lifetime will be over 1400 hours?

4) Let the random variable X follow a normal distribution with μ = 80 and σ2 = 100.

a. Find the probability that X is greater than 60. b. Find the probability that X is greater than 72 and less than 82. c. Find the probability that X is less than 55.

6) Anticipated consumer demand in a restaurant for free-range steaks next month can be modeled by a normal random variable with mean 1,200 pounds and standard deviation 100 pounds. a. What is the probability that demand will exceed 1,000 pounds? b. What is the probability that demand will be between 1,100 and 1,300 pounds?

1) A random variable is normally distributed with a mean of 50 and a standard deviation of 5.

a. What is the probability the random variable will assume a value between 45 and 55? b. What is the probability the random variable will assume a value between 40 and 60?

2) Golden Harvest produces high-quality organic frozen turkeys for distribution in organic food markets. The company has developed a range feeding program with organic grain supplements to produce their product. The mean weight of its frozen turkeys is 15 pounds with a variance of 4. Historical experience indicates that weights can be approximated by the normal probability distribution. Market research indicates that sales for frozen turkeys over 18 pounds are limited. a. What is the probability of the company’s turkey units will be over 18 pounds? b. What is the percentage of the company’s turkey units will be over 25 pounds?

4) To investigate how often families eat at home, Harris Interactive surveyed 500 adults living with children under the age of 18. The survey results are shown in the following table.

Number of Family Meals per Week - 0,1,2,3,4,5,6,7 or more.

Number of Survey Responses - 20,30,40,112,66,52,56,124.

For a randomly selected family with children under the age of 18, compute the following.

1. The probability of the family eats no meals at home during the week.
2. The probability of the family eats at least five meals at home during the week.
3. The probability of the family eats three or fewer meals at home during the week.

Consider tossing two coins.

1. Develop the sample space.

1) Let,

M = Event an officer is a man

W = Event an officer is a woman

A = Event an officer is promoted

B = Event an officer is not promoted

Suppose, a workforce consists of 1200 workers: 940 men and 240 women. Over the past two years, 324 officers were promoted: 288 males and 36 females.

1. What is the probability that a randomly selected officer is a man and is promoted?
2. What is the probability that a randomly selected officer is a man and is not promoted?
3. What is the probability that a randomly selected officer is a woman and is promoted?

5) At the end of performance evaluation period; the production manager found that 5 of the 50 workers completed work late, 6 of the 50 workers assembled a defective part, and 2 of the 50 workers completed work late and assembled a defective part. Suppose, L is the event that work is completed late and D is the event that assembled part is defective. a. Find P (L).b. Find P (D).c. Find P (L ∩ D).

7) Consider tossing two coins. a. Develop the sample space. b. Find out the probability of getting at least one head. c. What is the probability of getting two tails? d. What is the probability of getting one head?

8)An experiment has four equally likely outcomes: E1, E2, E3, and E4. a. What is the probability that E3 occurs? b. What is the probability that any two of the outcomes occur? c. What is the probability that any three of the outcomes occur?

Construct a 90% confidence interval for the true proportion of all employees of Big Star Ltd who believe that they deserve a salary increase, given that 80 out of a sample of 130 employees said that they believe that they deserve a salary increase.

Suppose that two machines I and II in a factory operate independently of each other. Past experience showed that during a given 8-hour time, machine I remains inoperative one third of the time and machine II does so about one fourth of the time. What is the probability that at least one of the machines will become inoperative during the given period?