Question

34​% 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

Answer:

Step-by-step explanation:

Given that 34​% of U.S. adults say they are more likely to make purchases during a sales tax holiday.

You randomly select 10 adults.

Let X be the no of adults in the selection of 10 who say they are more likely to make purchases during a sales tax holiday.

Each person is independent of the other and also there are two outcomes

Hence X is binomial with n =10 and p = 0.34

q = 0.66

P(X=r) $=10Cr (0.34)^r(0.68)^{10-r}$

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,

=$P(X=2)\\= 0.1873$

(b) more than​ two,

=$P(X>2)\\= 1-F(2)\\=1-0.2838\\= 0.7162$

(c) between two and​ five, inclusive.

=$P(2\leq x\leq 5)\\= F(5)-F(1)\\=0.9164-0.0965\\=0.8199$