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.

Interval ( 24 ; 40 ) has  136 participants

Interval ( 16 ; 40 ) has 163 participants

Step-by-step 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

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