Question

In: Statistics and Probability

If 15% of children in France play video games, what is the probability that fewer than...

If 15% of children in France play video games, what is the probability that fewer than 54 out of a random sample of 450 adults will play video games?

(round answer to nearest 3 decimal places)

Expert Solution

Probability of playing video games = p = 0.15 (15%=0.15)

Random Sample Size = n = 450

We will use Normal approximation to Binomial distribution in this case as sample size is quite large.

Let X denotes number of adults who play video games in the sample.

Mean = np = 450*0.15 = 67.5

Standard Deviation = = 7.575

We have to find the probability that fewer than 54 out of a random sample of 450 adults will play video games

i.e.

We get the phi value from Normal z table(attached).

The probability that fewer than 54 out of a random sample of 450 adults will play video games is 0.037

z table :

orchestra answered 2 years ago

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