Question

Suppose X is uniformly distributed on the interval [1,5]. You take a random sample of 36 of these, independently, and compute the sample mean X with bar on top. Compute the probability (two decimal places) that the sample mean is between 2.7 and 3.2.

Answer 1

Answer: the probability that the sample mean is between 2.7 and 3.2 is 0.13

Explanation:

The probability density function is expressed as

f(x) = 1/(b - a)

Where

b represents the highest value of x

a represents the lowest value of x

From the information given

b = 5

a = 1

Therefore,

f(x) = 1/(5 - 1) = 1/4 = 0.25

the probability that the sample mean is between 2.7 and 3.2 is expressed as

P(2.7 < x < 3.2)

It becomes

(3.2 - 2.7)0.25 = 0.5 × 0.25

= 0.13 rounded to 2 decimal places