One sixth of the students of a class joined the

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

Light travels at the speed of approximately 3.0 × 108 meters per second. Find the time in minutes required for light to travel f

expeople1 [14]

Speed = distance / time => time = distance / speed
speed = 3x10^8 x 60 = 180x10^8 m per minute
time = 1.5x10^11/180x10^8 = 150x10^9/180x10^8 = 5/6x10 = 8,3 minutes

6 0

3 years ago

Need help solving algebraic equations

svp [43]

Answer:

while whats the equation ?

Step-by-step explanation:

3 0

3 years ago

Solve this problem to find Y. 800 x Y = 4800

kupik [55]

Answer:

6

Step-by-step explanation:

800*Y=4800

Y=4800/800

Y=6

5 0

3 years ago

Read 2 more answers

Raymond is eight years older than Jeremiah. In 15 years, the sum of their ages will be 96 years. How old is each now?

Ivahew [28]

Answer:

In the present, Jeremiah would be 29 and Raymond, 37. As such, in 15 years, both of them would be 44 and 52 respectively, thus meaning their ages would equal 96.

Step-by-step explanation:

29 + 37 = 66

29 + 15 = 44

37 + 15 = 52

44 + 52 = 96

3 0

3 years ago