Mathematics, 15.04.2020 18:39 Kurlyash

A survey conducted for the Northwestern National Life Insurance Company revealed that 70% of American workers say job stress caused frequent health problems. 33 % said they expected to burn out in the job in the near future. Thirty-four percent said they thought seriously about quitting their job last year because of work-place stress. Fifty-three percent said they were required to work more than 40 hours a week very often or somewhat often.

a. Suppose a random sample of 15 American workers is selected. What is the expected number of these sampled workers who say they will burn out in the near future?

b. What is the probability that none of the workers say they will burn out in the near future?

c. What is the probability that at least two of the workers say they will burn out in the near future?

Answers: 3

Show answers

Answers

Answer from: Killion2022

a) The expected number is 5.

b) 0.25% probability that none of the workers say they will burn out in the near future

c) 97.93% probability that at least two of the workers say they will burn out in the near future

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they said they will burnout in the near future, or they did not. The probability of a person saying that they will burnout in the near future is independent of any other person. So the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

33 % said they expected to burn out in the job in the near future.

This means that p = 0.33

15 workers

This means that n = 15

a. Suppose a random sample of 15 American workers is selected. What is the expected number of these sampled workers who say they will burn out in the near future?

The expected number of the binomial distribution is given by the following formula:

E(X) = np

E(X) = 15*0.33 = 5

The expected number is 5.

b. What is the probability that none of the workers say they will burn out in the near future?

This is P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{15,0}.(0.33)^{0}.(0.67)^{15} = 0.0025$

0.25% probability that none of the workers say they will burn out in the near future

c. What is the probability that at least two of the workers say they will burn out in the near future?

Either less than two say this, or at least two do. The sum of the probabilities of these events is decimal 1. So

$P(X < 2) + P(X \geq 2) = 1$

We want $P(X \geq 2)$ . So

$P(X \geq 2) = 1 - P(X < 2)$

In which

P(X < 2) = P(X = 0) + P(X = 1)

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{15,0}.(0.33)^{0}.(0.67)^{15} = 0.0025$

$P(X = 1) = C_{15,1}.(0.33)^{1}.(0.67)^{14} = 0.0182$

P(X < 2) = P(X = 0) + P(X = 1) = 0.0025 + 0.0182 = 0.0207

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.0207 = 0.9793$

97.93% probability that at least two of the workers say they will burn out in the near future

Answer from: Quest

the answer to this question is 3/19

step-by-step explanation:

Answer from: Quest

answer: options

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 14:00, heatherswiffin666

Rewrite the following without an exponent. (5/8)-1

Answers: 1

continue

Mathematics, 21.06.2019 15:00, Chanman40025

The triangles are similar. what is the value of x? show your work.

Answers: 2

continue

Mathematics, 21.06.2019 15:30, CoreyHammond1517

Click on the y intercept. -x +4 i know you cant click on it so could you just say the coordinates like (example - (1,0) you so much.

Answers: 2

continue

Mathematics, 21.06.2019 16:20, kingalex7575

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria. the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time. create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

Answers: 1

continue

You know the right answer?

A survey conducted for the Northwestern National Life Insurance Company revealed that 70% of America...