Question

26​% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is​ (a) exactly​ two, (b) more than​ two, and​ (c) between two and​ five, inclusive.

Answer 1

a) p(X =2) = 0.261

b) P(x>2) = 0.566

c) P(2<x<5) = 0.334

Explanation:

Given 24% of U.S. adults say they are more likely to make purchases during a sales tax holiday

Probability 0f U.S. adults say they are more likely to make purchases during a sales tax holiday (p) = 0.24

n = 10

By using Poisson distribution

mean number of make purchases during a sales tax holiday

λ = np = 10 X 0.24 = 2.4

a)

The probability of getting exactly '2'

The probability

b) The probability of getting more than '2'

= 0.090 + 0.2177+0.261 = 0.566

P(x>2) = 0.566

c) The probability of getting between two and five

P( 2<x<5) = P(x=3)+p(x=4) =P(2<x<5) = 0.2090 + 0.125 = 0.334

hope this helps