According to defintion of compostion of functions, we can get:

But we know, that:

Our goal, is to express that function as a composition:

I.e:

If

then

. Hence,
The probability of making a type II error is given by one minus the power of the hypothesis test.
In general for the alternative hypothesis ,

The power of a hypothesis test is given by:

The probability of <span>making a type ii error when μ = 31,000 is given by

</span>
The answer is .004
Hope It Helps!
12% of 48 is equal to 5.76.
20% of 75 is 15
20% of 75+2 is 15.4
20% of 75+4 is 15.8
20% 0f 75+3 is 15.6
20% 0f 75+5 is 16
Hope this helped.
Answer:
Here, the formula would be:
P x (1 + rate)^50 = 1000000
With rate = 4.8% = 0.048, the money he needs to save today would be:
P = 1000000/(1 + 0.048)^50 = 95925.9$
Hope this helps!
:)