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Kipish [7]
3 years ago
6

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

rs.
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
Mathematics
1 answer:
Lelechka [254]3 years ago
5 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<x<31)
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<x<31)=0.9544
hence the number of members between that age was:
0.9544×300
=286.32 people
~285 People
Answer: 285 people

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