Question

Assume that when adults with smartphones are randomly​ selected, 59​% use them in meetings or classes. If 55 adult smartphone users are randomly​ selected, find the probability that at least 22 of them use their smartphones in meetings or classes. The probability is nothing. ​(Round to four decimal places as​ needed.)

Answer 1

P(an adult use smartphone in meetings or classes), p = 0.59

q = 1 - p = 0.41

Sample size, n = 55

P(X < A) = P(Z < (A - mean)/standard deviation)

For the given binomial distribution, Mean = np

= 55x0.59

= 32.45

Standard deviation =

=

= 3.6475

P(at least 22 of 55 use their smartphones in meetings or classes) = P(X 22)

= 1 - P(X < 21.5) (continuity correction of 0.5 is applied)

= 1 - P(Z < (21.5 - 32.45)/3.6475)

= 1 - P(Z < -3.00)

= 1 - 0.0013

= 0.9987