34%  of women consider themselves fans of professional baseball. You randomly select six women and ask each if she considers herself a fan of professional baseball.   Complete parts (a) through  (c)(a) Find  the mean of the binomial distribution.     _______  ( Round to the nearest tenth as needed)(b) Find the variance of the binomial distribution.     ________  ( Round to the nearest tenth as needed)(c) Find the standard deviation of the binomial distribution.     ________  ( Round to the nearest tenth  as needed.)Can  you please break this math problem down for me so I can understand better. Thank you.

Question
Asked Apr 30, 2019
158 views

34%  of women consider themselves fans of professional baseball. You randomly select six women and ask each if she considers herself a fan of professional baseball.   Complete parts (a) through  (c)

(a) Find  the mean of the binomial distribution.

     _______  ( Round to the nearest tenth as needed)

(b) Find the variance of the binomial distribution.

     ________  ( Round to the nearest tenth as needed)

(c) Find the standard deviation of the binomial distribution.

     ________  ( Round to the nearest tenth  as needed.)

Can  you please break this math problem down for me so I can understand better. Thank you.

check_circle

Expert Answer

Step 1

Introduction:

Let X denotes the number of women who consider themselves as fans of professional baseball, in the sample.

Now, when a woman is asked whether she is a fan or not, there may be two responses: “yes” and “no”. Consider the response yes as a “success” and the response no as a “failure”.

As 34% are self-proclaimed fans of professional baseball, the probability of “success” is 34% or 0.34. Denote this probability of success as p. So, p = 0.34.

The sample collected is of size 6, so that, n = 6. It is safe to assume that the response of one woman in the sample (regarding, whether she is a baseball fan or not) is independent of that of another. So, the probability of success is the same for all women sampled.

Now, if the possible outcomes of a trial can be classified as a “success” and a “failure” and the probability of success of each trial, p is a constant, then, for n of those trials, the number of successes, X has a Binomial distribution with parameters n and p. The mean or expectation of the Binomial random variable is np and the variance is np(1 – p).

Step 2

Parts a, b and c:

a:

The mean of the Binomial distribution is: np = 6 ∙ (0.34) = 2.04 ≈ 2.0 (to the nearest tenth).

b:

The variance of the Binomial distribution is: np(1 – p) = 6 ∙ (0.34) ∙ (1 – 0.34) = 6 ∙ (0.34) ∙ (0.66) = 1.3464 ≈ 1.3 (to the nearest tenth).

c:

The standard deviatio...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: The Toylot company makes an electric train with a motor that it claims will draw an average of only ...

A: The provided information are:

question_answer

Q: The table below shows the critical reading scores for 14 students the first two times they took a st...

A: Given the data of critical reading scores for 14 students the first two times they took a standardiz...

question_answer

Q: Listed below are brain volumes, measured in cubic centimeters, of twins at birth. Use a 5% significa...

A: Solution:Null and alternative hypotheses:Null hypothesis: µ1 − µ2 = 0 (equivalently µ1 = µ2)Alternat...

question_answer

Q: Var Adn Cater Graded Assignment 3 ue: 08/01 Plesse, show your work ond write your answers in full se...

A: Preliminary calculations:The probability distribution is constructed as follows.

question_answer

Q: According to a random sample taken at 12 A.M., body temperatures of healthy adults have a bell-shape...

A: Chebyshev’s inequality:Chebyshev’s rule is appropriate for any distribution. That is, Chebyshev’s in...

question_answer

Q: Simple random sampling uses a sample of size from a population of size to obtain data that can be us...

A: The population size is denoted by ‘N’ and the sample size is denoted by ‘n’.Let the number of differ...

question_answer

Q: Please answer the attached picture. Thanks,

A: Г(1,Ɵ) represents a gamma distribution X~ Г(α,λ) where α is the shape parameter and λ is the scale p...

question_answer

Q: For frecuency distribution for us governor 2019.  Party.                     Frequency Democratic.  ...

A: Given question have more than three sub parts. According to our policies cannot answer more than thr...

question_answer

Q: Natasha is a physician looking to determine whether a supplement is effective in helping men lose we...

A: Test statistic results:For testing whether a supplement is effective in helping men lose weight or n...