Answer to Question #185142 in Statistics and Probability for nini

Question

A chicken rice chain store conducted a taste survey before marketing its’

newly tasted chicken rice. The results of the survey showed that 85% of the

people who tried this new chicken rice liked it. Excited by this result, the

chain store decided to market this newly taste chicken rice. On a certain day,

ten customers bought this chicken rice for the first time.

Find the probability that exactly four of the customers will like the

chicken rice.

Answer 1

Probability that people like chicken rice = 85% $= 0.85 = p$

Probability that people not like chicken rice = 25% $= 0.25 = q$

n = 10

Using the Binomial distibtution,

$P(x) = ^{10}C_x(p)^{10-x}q^x$

Probability that exactly four of the customers will like the

chicken rice.

$= P(4)$

$= ^{10}C_4(0.85)^{6}0.25^4$

$= 0.30$