Question

Given a random sample of size 24 from a normal distribution, find k such that (a) p(−2.069

Answer 1

The graph of the normal distribution of the random sample size of 24 will have the shape of a bell curve.

The value of k such that P(-2.069 < T < k) = 0.965 is 2.5

How to determine the value of k?

The sample size is given as:

n = 24

This means that the degrees of freedom is:

df = n - 1

df = 24 - 1

df = 23

The probability is given as:

P(-2.069 < T < k) = 0.965

This can be rewritten as:

P(T>-2.069) - P(T>k) = 0.965

The value of P(T>-2.069) at a degrees of freedom of 23 and $\alpha$ = 0.025 is 0.975

So, we have:

0.975 - P(T>k) = 0.965

Collect like terms

P(T>k) = 0.975 - 0.965

Evaluate the difference

P(T>k) = 0.01

The value of k that makes P(T>k) = 0.01 is 2.5.

So, we have:

k = 2.5

Hence, the value of k is 2.5

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