A computer selects a number
X
X
from 4 to 11 randomly and uniformly. Round all answers to 4 decimal places where possible.
What is the distribution of
X
X
?
X
X
~ U(,)
Suppose that the computer randomly picks 35 such numbers. What is the distribution of
¯
x
x
¯
for this selection of numbers.
¯
x
x
¯
~ N(,)
What is the probability that the average of 35 numbers will be less than 7.9?

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jayfeatherforlife jayfeatherforlife · Answer 1 · 2021-10-20T13:11:57+02:00

Answer:

22.5

Step-by-step explanation:

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priyankapandeyVT priyankapandeyVT · Answer 2 · 2022-07-20T11:19:48+02:00

The required Distribution, selection and probability is X to U(4,11), x to N (7.5, 0.3415) and 0.87932 respectively.

(a) Distribution of X is uniform distribution X to U(4,11).

(b) Sample size (n) = 35, distribution of mean would be moderate with value = (4+11)/2 = 7.5

Standard deviation = √ [(11-4)^2/(12*35] = 0.3415
Now
x to N (7.5, 0.3415)

(c) We have to find probability that the average of 35 numbers will be less than 7.9.

P(x < 7.9) = P(x < 7.9; 7.5; 0.3415)
Z = (7.9 -7.5)/0.3415
Z = 1.1713
P(x< 7.9)= P(Z < 1.1713)= 0.87932.

Thus, The required Distribution, selection and probability is X to U(4,11), x to N (7.5, 0.3415) and 0.87932 respectively.

Learn more about probability here:

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