Sara Gordon is heading a fund raising drive for a college. She wishes to concentrate on the current 10th reunion class and hopes to get contributions from 36% of the 250 members of that class. Past data indicate that those who contribute to the 10th year reunion will donate 4% of their annual salaries. Sara believes that the reunion class members' average salaries have an avg of 32000 dollars and a std. deviation of 9600 dollars. If her expectations are met (36% of class contributing 4% of their salaries), what is the probability that the reunion gift will be between 110000 dollars and 120000 dollars? Should I take the std error of sampling distribution and calculate the z score? If I do that, the z score comes to ~ 6.1

Belen Moses

Belen Moses

Open question

2022-08-20

Sara Gordon is heading a fund raising drive for a college. She wishes to concentrate on the current 10th reunion class and hopes to get contributions from 36% of the 250 members of that class. Past data indicate that those who contribute to the 10th year reunion will donate 4% of their annual salaries. Sara believes that the reunion class members' average salaries have an avg of 32000 dollars and a std. deviation of 9600 dollars. If her expectations are met (36% of class contributing 4% of their salaries), what is the probability that the reunion gift will be between 110000 dollars and 120000 dollars?
Should I take the std error of sampling distribution and calculate the z score? If I do that, the z score comes to 6.1

Answer & Explanation

Kaeden Bishop

Kaeden Bishop

Beginner2022-08-21Added 15 answers

If X is the distribution of the donation,
E [ X ] = 32 , 000 25 = 1 , 280
σ X = 9 , 600 2 25 2 = 384
Now, if 36% of the 250 guys donate, you have that 90 guys donate.
Let's Y indicate the distribution of the sum donated, we have
E [ Y ] = 1 , 280 × 90 = 115 , 200
σ Y = 384 2 × 90 3 , 643
As 90 is large enough you can use the gaussian approx and thus your expected probability is
P [ 110 , 000 < Y < 120 , 000 ] = Φ [ 120 , 000 115 , 200 3 , 643 ] Φ [ 110 , 000 115 , 200 3 , 643 ] =
= Φ [ 1.32 ] Φ [ 1.43 ] 83 %

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