Question

59​% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is ​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four.

Answer 1

Proportion of adults that have very little confidence in newspaper, p = 0.59

Sample size, n = 10

X~ Binomial(10, 0.59)

a) Probability that exactly 5 have very little confidence, P(X =5) =

Using binomial function in excel:

=BINOM.DIST(5, 10, 0.59, 0)

= 0.2087

b) Probability that at least 6 have very little confidence, P(X >= 6) = 1-P(X<6)

= 1-P(X<=5)

Using binomial function in excel:

= 1 - BINOM.DIST(5, 10, 0.59, 1)

= 1 - 0.3922 = 0.6078

c) Probability that less than 4 have very little confidence, P(X < 4) = P(X <= 3)

= P(X<= 3)

Using binomial function in excel:

= BINOM.DIST(3, 10, 0.59, 1)

= 0.0626