Evaluate 5x - 4y when x =

A survey conducted for the Northwestern National Life Insurance Company revealed that 70% of American workers say job stress cau

Bad White [126]

Answer:

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:

$E(X) = np$

So

$E(X) = 15*0.33 = 5$

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

3 0

3 years ago

is it possible to store a 20 foot long pipe in a rectangular room that is 10 feet by 12 feet by 8 feet?

Anastaziya [24]

First we'll consider the floor size.
In a 10 by 12 room the longest pipe that will fit lying on the floor equals the hypotenuse of a 10 by 12 triangle:
hypotenuse² = 10² + 12²
hypotenuse² = 100 + 144
hypotenuse² = 244
hypotenuse = 15.62 feet

Now we have to consider the third dimension (height = 8 feet).
The two sides would be 15.62 and 8
hypotenuse² = 15.62² + 8²
hypotenuse² = 244 + 64 = 308
hypotenuse = 17.55
So, the longest pipe that would fit in that room would be 17.55 feet long.

7 0

3 years ago

Read 2 more answers

PLZ DO THIS PLZ PLZ PLZ I WILL MARK THE BRAINLIEST

Elodia [21]

Answer:

188,582 fewer people attended the 2010 olympics to the 2006 olympics.

Step-by-step explanation:

Add all of the 2010 matches then subtract from 2006 total. You will get a negative number. Hope I helped!:-)

8 0

4 years ago

Solve 5x=45 using the opposite operation