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?

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285

Question

Mathematics

Kaliyah Hoffman

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)

Know the Answer?

Allie Esparza · Answer 1

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

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?204264270285

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