1.
X: Number of pizzas consumed
X follows normal distribution with mean 12 and standard deviation 5
A.
Proportion of students consume more than 14 pizzas per month = P(X>14)
P(X>14) = 1 - P(X
14)
Z-score for 14 = (14-12)/5 = 2/5 = 0.4
from standard normal tables, P(Z0.4)
= 0.6554
P(X
14)=P(Z
0.4)
= 0.6554
P(X>14) = 1 - P(X
14) = 1 - 0.6554 = 0.3446
Proportion of students consume more than 14 pizzas per month = 0.3446
B.
If X follows a normal distribution with mean
and standard deviation
, then by central limit theorem, sampling distribution of sample
mean(sample size:n) follows normal distribution with mean
and standard deviation:
Therefore,
:sample Average number of pizzas consumed by 8 students : follow
normal distribution with mean 12 and standard deviation =
= 1.7678
Probability that , in a random sample of 8 students, a sample
average of more than 10 pizzas are consumed = P(
> 10)
P(
> 10) = 1-P(
)
Z-score of 10 =(10-12)/1.7678 = -1.13
from standard normal tables, P(Z-1.13)
= 0.1292
P()
= P(Z
-1.13)
= 0.1292
P(
> 10) = 1-P(
)
= 1-0.1292=0.8708
Probability that , in a random sample of 8 students, a sample average of more than 10 pizzas are consumed = 0.8708
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