PRACTICE OF STATISTICS F/AP EXAM
PRACTICE OF STATISTICS F/AP EXAM
6th Edition
ISBN: 9781319113339
Author: Starnes
Publisher: MAC HIGHER
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Question
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Chapter 6.3, Problem 84E

(a)

To determine

The number of times the light is red is a binomial random variable.

(a)

Expert Solution
Check Mark

Answer to Problem 84E

Since all four conditions have been satisfied, Y is a binomial random variable.

Explanation of Solution

Given information:

Number of trials, n=10

Probability of success, p=55%=0.55

Y : The number of times that the light is red.

For the binomial random variable,

The four conditions are as follows:

Binary: Since the success resembles the light is red and failure resembles the light is not is not red. Thus, the condition is satisfied.

Independent trials: It is known that Pedro’s working days are chosen at random. Thus, the condition has been satisfied.

Fixed number of trials: Since we chose 10 Pedro’s work days. Thus, the number of trials is 10 and the condition has been satisfied.

Probability of success: Since there are 55% chances for the light to be red. Thus, the probability for the light to be red is 55% and the condition has been satisfied.

Hence,

All the conditions are satisfied.

According to this scenario,

Y describes a binomial setting.

(b)

To determine

Probability for the light is red on exactly 7 days.

(b)

Expert Solution
Check Mark

Answer to Problem 84E

The probability that the light is red on exactly 7 days is approx. 0.1665.

Explanation of Solution

Given information:

Number of trials, n=10

Probability of success, p=55%=0.55

According to the binomial probability,

  P(X=k)=(nk)pk(1p)nk

At k=7 ,

The binomial probability to be evaluated as:

  P(X=7)=(107)(0.55)7(10.55)107=10!7!(107)!(0.55)7(0.45)3=120(0.55)7(0.45)30.1665=16.65%

Thus,

Around 16.65% chances are there for the light to be red on exactly 7 days and the probability is approx. 0.1665.

Chapter 6 Solutions

PRACTICE OF STATISTICS F/AP EXAM

Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - Prob. 49ECh. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Prob. 56ECh. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Prob. 61ECh. 6.2 - Prob. 62ECh. 6.2 - Prob. 63ECh. 6.2 - Prob. 64ECh. 6.2 - Prob. 65ECh. 6.2 - Prob. 66ECh. 6.2 - Prob. 67ECh. 6.2 - Prob. 68ECh. 6.2 - Prob. 69ECh. 6.2 - Prob. 70ECh. 6.2 - Prob. 71ECh. 6.2 - Prob. 72ECh. 6.2 - Prob. 73ECh. 6.2 - Prob. 74ECh. 6.2 - Prob. 75ECh. 6.2 - Prob. 76ECh. 6.3 - Prob. 77ECh. 6.3 - Prob. 78ECh. 6.3 - Prob. 79ECh. 6.3 - Prob. 80ECh. 6.3 - Prob. 81ECh. 6.3 - Prob. 82ECh. 6.3 - Prob. 83ECh. 6.3 - Prob. 84ECh. 6.3 - Prob. 85ECh. 6.3 - Prob. 86ECh. 6.3 - Prob. 87ECh. 6.3 - Prob. 88ECh. 6.3 - Prob. 89ECh. 6.3 - Prob. 90ECh. 6.3 - Prob. 91ECh. 6.3 - Prob. 92ECh. 6.3 - Prob. 93ECh. 6.3 - Prob. 94ECh. 6.3 - Prob. 95ECh. 6.3 - Prob. 96ECh. 6.3 - Prob. 97ECh. 6.3 - Prob. 98ECh. 6.3 - Prob. 99ECh. 6.3 - Prob. 100ECh. 6.3 - Prob. 101ECh. 6.3 - Prob. 102ECh. 6.3 - Prob. 103ECh. 6.3 - Prob. 104ECh. 6.3 - Prob. 105ECh. 6.3 - Prob. 106ECh. 6.3 - Prob. 107ECh. 6.3 - Prob. 108ECh. 6.3 - Prob. 109ECh. 6.3 - Prob. 110ECh. 6.3 - Prob. 111ECh. 6.3 - Prob. 112ECh. 6.3 - Prob. 113ECh. 6.3 - Prob. 114ECh. 6.3 - Prob. 115ECh. 6.3 - Prob. 116ECh. 6.3 - Prob. 117ECh. 6.3 - Prob. 118ECh. 6.3 - Prob. 119ECh. 6 - Prob. R6.1RECh. 6 - Prob. R6.2RECh. 6 - Prob. R6.3RECh. 6 - Prob. R6.4RECh. 6 - Prob. R6.5RECh. 6 - Prob. R6.6RECh. 6 - Prob. R6.7RECh. 6 - Prob. R6.8RECh. 6 - Prob. T6.1SPTCh. 6 - Prob. T6.2SPTCh. 6 - Prob. T6.3SPTCh. 6 - Prob. T6.4SPTCh. 6 - Prob. T6.5SPTCh. 6 - Prob. T6.6SPTCh. 6 - Prob. T6.7SPTCh. 6 - Prob. T6.8SPTCh. 6 - Prob. T6.9SPTCh. 6 - Prob. T6.10SPTCh. 6 - Prob. T6.11SPTCh. 6 - Prob. T6.12SPTCh. 6 - Prob. T6.13SPTCh. 6 - Prob. T6.14SPT
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