SOLUTION: 1. The annual per capita consumption of ice cream​ (in pounds) in the United States can be approximated by a normal distribution with mean of 14 lbs and a standard deviation

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Question 1072194: 1. The annual per capita consumption of ice cream​ (in pounds) in the United States can be approximated by a normal distribution with mean of 14 lbs and a standard deviation of 2.1 lbs.

a. What percent of the population consumes at most 10 lbs​ yearly?
b. Jack estimates that​ 24% of the population eats more ice cream than he does. Find how much ice cream he eats per year.
c. Between what two values does the middle​ 80% of the consumption​ lie?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The annual per capita consumption of ice cream​ (in pounds) in the United States can be approximated by a normal distribution with mean of 14 lbs and a standard deviation of 2.1 lbs.
a. What percent of the population consumes at most 10 lbs​ yearly?
z(10) = (10-14)/2.1 = -1.9047
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Find the percentage below that z-value
P(x <= 10) = P(z <= -1.9047) = normalcdf(-100,-1.9047) = 0.0284
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b. Jack estimates that​ 24% of the population eats -more ice cream than he does. Find how much ice cream he eats per year.
Find the z-value with a right tail of 0.24
invNorm(0.76) = 0.7063
Find the corresponding raw score value::
x = 0.7063*2.1 + 14
x = 15.48 lbs (Amt. he consumes yearly)
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c. Between what two values does the middle​ 80% of the consumption​ lie?
Find the z-value with a left tail of 10%
invNorm(0.1) = -1.2816
Find the correspond lbs at +1.2816 and -1.2816
x = 1.2816*2.1+14 and x = -1.2816*2.1+14
Those are the upper and lower limits of the interval.
Cheers,
Stan H.
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