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Get Full Access to Elementary Statistics - 12 Edition - Chapter 5.4 - Problem 2bsc
Get Full Access to Elementary Statistics - 12 Edition - Chapter 5.4 - Problem 2bsc

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# Standard Deviation For the binomial distribution described ISBN: 9780321836960 18

## Solution for problem 2BSC Chapter 5.4

Elementary Statistics | 12th Edition

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Problem 2BSC

Standard Deviation For the binomial distribution described by the conditions in Exercise 1, find the standard deviation by evaluating n p q . Some books use the expression n p ( 1 − p ) for the standard deviation. Will that expression always yield the same result?

Step-by-Step Solution:
Step 1 of 3

Problem 2BSC

Step1 of 3:

We have Standard Deviation For the binomial distribution described by the conditions in Exercise 1, find the standard deviation by evaluating Some books use the expression for the standard deviation.

“Yes”,this expression always yield the same result.

Step2 of 3:

We have In a clinical trial of the cholesterol drug Lipitor, 270 subjects were given a placebo, and 7% of them developed headaches. For such randomly selected groups of 270 subjects given a placebo,we need to identify the values of n, p, and q that would be used for finding the mean and standard deviation for the number of subjects who develop headaches.

Consider a random variable “x” follows binomial distribution with sample size “n” and proportion “p”.

i,e.X B(n, p)

Where,

n = 270 and p = 0.07.

q = 1 - p

= 1 - 0.07.

= 0.93

Probability mass function of binomial distribution is given by

P(x) = , x = 0,1,2,...,n.

With mean E(x) = np and variance var(x) = npq

Consider,

E(x) = np

= 270 0.07

= 18.9

Therefore,E(x) = 18.9

var(x) = npq

= 270 0.07 0.93

= 17.577

Step3 of 3:

Standard deviation is given by = = = 4.1924. 4 people.

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321836960

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