Assume that when adults with smartphones are randomly selected, 5858% use them in meetings or classes. If 66 adult smartphone users are randomly selected, find the probability that at least 44 of them use their smartphones in meetings or classes. In a binomial probability distribution, probabilities can be calculated by using technology, a table of binomialprobabilities, or the binomial probability formula, shown below where n is the number of trials, x is the number of successes among n trials, p is the probability of success in any one trial, and q is the probability of failure in any one trial left parenthesis q equals 1 minus p right parenthesis .(q=1−p). Upper P left parenthesis x right parenthesisP(x)equals=StartFraction n exclamation mark Over left parenthesis n minus x right parenthesis exclamation mark x exclamation mark EndFraction times p Superscript x Baseline times q Superscript n minus xn!(n−x)!x!•px•qn−x, for xequals=0, 1, 2,..., n To use this formula to evaluate the probability of Xgreater than or equals≥x successes or Xless than or equals≤x successes, find the sum of P(x) for all values of X that satisfy the inequality. Identify the values of n, x, and p. nequals=66 , xequals=44 , pequals=. 58.58 (Type an integer or a decimal. Do not round.) The statement "at least 44" corresponds to the inequality Upper X greater than or equals 4.X≥4. Substitute the values for n, x, and p into technology for each possible value of x greater than or equal to 44 to find each probability. Then sum to find Upper P left parenthesis Upper X greater than or equals 4 right parenthesisP(X≥4).

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...

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Question

Assume that when adults with smartphones are randomly selected,

5858%

use them in meetings or classes. If

adult smartphone users are randomly selected, find the probability that at least

of them use their smartphones in meetings or classes.

In a binomial probability distribution, probabilities can be calculated by using technology, a table of binomialprobabilities, or the binomial probability formula, shown below where n is the number of trials, x is the number of successes among n trials, p is the probability of success in any one trial, and q is the probability of failure in any one trial

left parenthesis q equals 1 minus p right parenthesis .(q=1−p).

Upper P left parenthesis x right parenthesisP(x)equals=StartFraction n exclamation mark Over left parenthesis n minus x right parenthesis exclamation mark x exclamation mark EndFraction times p Superscript x Baseline times q Superscript n minus xn!(n−x)!x!•px•qn−x,

for

xequals=0,

1, 2,..., n

To use this formula to evaluate the probability of

Xgreater than or equals≥x

successes or

Xless than or equals≤x

successes, find the sum of P(x) for all values of X that satisfy the inequality.

Identify the values of n, x, and p.

nequals=66

xequals=44

pequals=. 58.58

(Type an integer or a decimal. Do not round.)

The statement "at least

44"

corresponds to the inequality

Upper X greater than or equals 4.X≥4.

Substitute the values for n, x, and p into technology for each possible value of x greater than or equal to

to find each probability. Then sum to find

Upper P left parenthesis Upper X greater than or equals 4 right parenthesisP(X≥4).

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