Question

The data below relates to questions 09, 10 and 11

A recent study was conducted to determine how many individuals had at least an X-Box One, Play Station 4 and Nintendo Switch (Video Game System) at home.   The survey included 800 individuals.

The age group of the 800 individuals is listed below:

Age Group	Percentage
Under 18	18%
18 to 59	53%
60 +	29%

Utilize the normal approximation of the binomial distribution to answer the questions below.  Use the Continuity Correction Factor.

Requirement:

Assume the sample is now 600, compute the probability that fewer than 100 will be under that age of 18.

Your answer should be to four decimals.

Please help! Every time when I submit this question everyone gets it wrong!

Answer 1

The number of individuals in the sample of 600 individuals who would be under age of 18 here is modelled as:

This is approximated by a normal random variable as:

The probability that fewer than 100 will be under that age of 18 is computed here as:
P(X < 100)

Applying the continuity correction factor, we have here:
P(X < 99.5)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.1832 is the required probability here.