Question

There is a chowder eating contest in a small New England town. The distribution of the amount of chowder consumed is bell-shaped with mean 32 ounces and variance 64 ounces. If two hundred people participated in the contest, find the following.a. The number of people who consumed between 24 and 40 ounces of chowder.b. The number of people who consumed between 16 and 40 ounces of chowder.

Answer 1

Interval ( 24 ; 40 ) has 136 participants

Interval ( 16 ; 40 ) has 163 participants

Explanation:

Normal distribution.

As variance is 64 then standard deviation is σ = 8

And mean μ₀ = 32

We can see that μ₀ ± σ is 32 ± 8

The interval ( 32- 8 ; 32+8 ) is ( 24 ; 40 )

By empirical Rule we know that μ₀ ± σ contains 68% of the population then 200*0,68 = 136

The number of participants between 24 and 40 is 136

By symmetry of these 136 half of them are between 32 and 40 ( 136/2 = 68 ) ( between mean and 40 )

Now in the interval ( 16 ; 40 ) we note that 16 is 32 - 16 = 16 or μ₀ - 2σ

And again by empirical rule μ₀ ± 2σ has 95 % of the population that means 200*0.95 = 190 and by symmetry 190/2 95 are between μ₀ - 2σ, therefore

95 people are between μ₀ - 2σ or between ( 16 ; 32 ) and between ( 32 ; 40 ) there are 68 people then

The interval ( 16 ; 40 ) has 95 + 68 = 163 participants