Overall, the amount of calories from ice-cream consumed is normally distributed
ID: 3178070 • Letter: O
Question
Overall, the amount of calories from ice-cream consumed is normally distributed around 350 calories with a standard deviation of 25 calories.
What’s the probability that the mean calories amount consumed will be between 200 and 300?
In looking to promote good healthy eating, the ice-cream flavors whose calorie amounts are in the top 4% will have their price increased by 10%.
For the same reason, healthy life style, the customers at or below the 15%ile of calories amount consumed, will receive 2 weeks free membership at Ballys. What is the maximum amount of calories that you should consume in order to receive the free membership.
How likely (what is the probability) is it to have the amount calories between 400 and 450?
How likely (what is the probability) is it that Frosty (name not previously mentioned) will consume more than 300 calories?
What percentile does a 350 calories rank at?
If 16 people ( 16 = size of the sample) selected randomly buy ice-cream what’s the likelihood that their mean calories amount will be within 15 calories of the population mean? (population mean +/- 15)
What’s the probability that the mean calories amount consumed will be between 200 and 300?
In looking to promote good healthy eating, the ice-cream flavors whose calorie amounts are in the top 4% will have their price increased by 10%.
For the same reason, healthy life style, the customers at or below the 15%ile of calories amount consumed, will receive 2 weeks free membership at Ballys. What is the maximum amount of calories that you should consume in order to receive the free membership.
How likely (what is the probability) is it to have the amount calories between 400 and 450?
How likely (what is the probability) is it that Frosty (name not previously mentioned) will consume more than 300 calories?
What percentile does a 350 calories rank at?
If 16 people ( 16 = size of the sample) selected randomly buy ice-cream what’s the likelihood that their mean calories amount will be within 15 calories of the population mean? (population mean +/- 15)
Explanation / Answer
All answers:
We have been given params of normal dist:
Mean = 350
Stdev = 25
a. P(200<X<300) = P(-6<Z<-2) = .023
b. P(X=x) = .96, Z=1.75, hence, X = 1.75*25+350 = 393.75
c. P(X=x ) = .15, Z=-1.04, x = -1.04*25+350 = 324
d. P(400<X<450) = P(2<X<4) = .999-.977 = .022
e. P(X<300) = P(Z<-2) = .023
f. P(X=350 ) =.5 ( Hence its the median or 50th percentile)
g. n=16, P(|X-x|<=15) = P(Z<= 15/(25/sqrt(16)) =P(Z<2.4) =.9918
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