Mathematics: According to a candy company, packages of a certain candy contain 24% orange candies. find the approximate probability that the random sample of 200 candies will contain 26% or more orange candies.

According to a candy company, packages of a certain

pennygillbert

11.01.2022

0.3720

Step-by-step explanation:

Given that according to a candy company, packages of a certain candy contain 24% orange candies.

As per central limit theorem we find that samples will have mean proportin same as population proportion with std deviation sqrt (pq/n)

$p=0.25\\q=1-p =0.75\\n = 200\\std dev =\sqrt{\frac{pq}{n} } \\=0.0306$

i.e. Sample proportion is normal with mean= 0.25 and std dev = 0.0306

Required probability

=probability that the random sample of 200 candies will contain 26% or more orange candies.

=P(p>0.26)

= $P(Z\frac{0.26-0.25}{0.0306} \\=P(Z0.327)\\=0.3720$

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