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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
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 [tex]\alpha[/tex] = 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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