Question

Sports and Leisure. The reality television series Splash! features celebrities attempting to learn how to dive. The first episode aired in January 2013 and earned a 23.6% audience share. That is, 23.6% of all TVs in use during the show time period were tuned to a station airing Splash!. 24 people who watched TV during that time period were selected at random.

(a) Find the probability (±0.0001) that at least six watched Splash! P(X⩾6) = .9600

(b) Find (±0.0001) the expected number of people who watched Splash!. μ = 5.664

(c) Find the probability (±0.0001) that the number of people who watched Splash! is less than the mean. P(X<μ) =

(d) Suppose that at most three people watched Splash!What is the probability (±0.0001) that no one watched Splash! ? P(X=0|X⩽3) =

Answer 1

Probability that people watched Splash, p = 0.236

Number of people, n = 24

a) Probability that atleast 6 watched Splash, P(X>=6) = 1-P(X<6)

= 1-P(X<=5)

Using binomial function in excel:

= 1- BINOM.DIST(5, 24, 0.236, 1)

= 0.5141

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b) Expected number of people who watched Splash =

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c) Probability that the number of people who watched Splash is less than the mean, P(X< 5.664) = P(X <= 5)

Using binomial function in excel:

= BINOM.DIST(5, 24, 0.236, 1)

= 0.4859

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(d) Probability that at most 3 people watched splash, P(X<=3) =

Using binomial function in excel:

= BINOM.DIST(3, 24, 0.236, 1)

= 0.147654

Probability that no one and at most 3 People watched the Splash, P((X=0)&(X<=3) = P(X=0)

Using binomial function in excel:

= BINOM.DIST(0, 24, 0.236, 1)

= 0.001564

Probability that no one watched Splash give that atmost 3 watched, P(X=0|X<=3) =