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22 August, 13:13

The ages of members of an online gaming group are normally distributed with a mean of 23 years and a standard deviation of 4 years.

There are 300 members in the group.

About how many members are expected to be between 15 years old and 31 years old?

204

264

270

285

+3
Answers (1)
  1. 22 August, 14:22
    0
    To get the number of members between 15 years and 30 years we proceed as follows:

    z = (x-μ) / σ

    where:

    mean,μ=23

    standard deviation, σ=4 years

    thus

    P (15
    when x=15

    P (x<15)

    z = (15-23) / 4

    z=-2

    thus

    P (x<15) = P (z<-2) = 0.0228

    when x=31

    z = (31-23) / 4

    z=2

    thus

    P (x<31) = P (z<2) = 0.9772

    Hence:

    P (15
    hence the number of members between that age was:

    0.9544*300

    =286.32 people

    ~285 People

    Answer: 285 people
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