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.

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

Step-by-step 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

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