After being rejected for employment, Kim Kelly learns that the Bellevue Credit C

Cem Hayes 2021-10-02 Answered
After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only two women among the last 19 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women.
Help her address the charge of gender discrimination by finding the probability of getting two or fewer women when 19 people are hired, assuming that there is no discrimination based on gender.
(Report answer accurate to 8 decimal places).

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Margot Mill
Answered 2021-10-03 Author has 9453 answers

Step 1
The binomial probability distribution is,
\(P(X=x)=\left(\begin{array}{c}n\\ x\end{array}\right)(p)^{x}(1-p)^{n-x}\)
In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.
Let x be the number of women hired which follows binomial with sample size 19 and probability of success \(\displaystyle{0.5}{\left(={\frac{{{1}}}{{{2}}}}\right)}\)
Step 2
The probability of getting two or fewer women when 19 people are hired is,
\(\displaystyle{P}{\left({X}\leq{2}\right)}={P}{\left({X}={0}\right)}+{P}{\left({X}={1}\right)}+{P}{\left({X}={2}\right)}\)
\(=\left(\begin{array}{c}19\\ 0\end{array}\right)(0.5)^{0}(1-0.5)^{19-0}+\left(\begin{array}{c}19\\ 1\end{array}\right)(0.5)^{1}(1-0.5)^{19-1}+\left(\begin{array}{c}19\\ 2\end{array}\right)(0.5)^{2}(1-0.5)^{19-2}\)
\(\displaystyle={0.00000191}+{0.00003624}+{0.00032616}\)
\(\displaystyle={0.00036431}\)
Thus, the probability of getting two or fewer women when 19 people are hired is 0.00036431.

Have a similar question?
Ask An Expert
43
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-05-25

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution.

\(\begin{bmatrix}1 & -4&5 \\0 & 0&0 \\0 & 0&0 \\ \end{bmatrix}\)

asked 2021-05-26
3,645 rolls of landscape fabric are manufactured during one day. After being inspected, 121 of these rolls are rejected as imperfect. What percent of the rolls is rejected? (Round to the nearest whole percent.)
asked 2021-09-18
34% of college students say they use credit cards because of rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two, and (c) between two and five include. If convenient, use technology to find the probabilities.
\(\displaystyle{\left({a}\right)}{P}{\left({2}\right)}=?\)
asked 2021-06-22
A bank wants to know which of two incentive plans will most increase the use of its credit cards. It offers each incentive to a group of current credit card customers, determined at random, and compares the amount charged during the following six months. What type of study design is being used to produce data?
asked 2021-09-15
The Mean for a Binomial Distribution is
A) p
B) q
C) np
D) npq
asked 2021-06-10

the function P represent the population \(P(d)\), in thousands, of a colony of insects d days after first being measured. A model for \(P\) is \(P(d) = 10 \cdot (1.08)^d\)

a) There were 1,080 Insects when the colony was first counted.

b) One week after the colony was first counted, there were 10,800 insects.

c) The growth factor per day is \(1.08\)

d)  The growth factor per week is \(1.80 \cdot 7\)

e) The growth factor per hour is \(1.08^{\frac{1}{34}}\)

 

asked 2021-09-15
Consider an acceptance sampling plan with \(\displaystyle{n}={20}\ {\quad\text{and}\quad}\ {c}={0}\). Compute the producer’s risk for each of the following cases.
a. The lot has a defect rate of 2%

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question
...