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Answer:
a) Proportion = 41.3%
b) Proportion = 9.18%
c) Proportion = 13.35%
d) Interest payment = $37.28
Explanation:
We have normal distribution with mean = 29 and standard deviation = 9
a) The proportion of the bank’s Visa cardholders pay more than $31 in interest is:
P(X > 31) = = P (Z > 0.22) = 1 - P (Z ≤ 0.22) =
1 - 0.58706 = 0.41294 = 41.3%
The proportion of the bank's Visa cardholders pay more than 31 dollars in interest is 41.3%.
b) The proportion of the bank’s Visa cardholders pay more than $31 in interest is:
P(X > 41) = = P (Z > 1.33) = 1 - P (Z ≤ 1.33) =
1 - 0.90824 = 0.09176 = 9.176% ≈ 9.18%
The proportion of the bank's Visa cardholders pay more than 31 dollars in interest is 9.18%.
c) The proportion of the bank’s Visa cardholders pay more than $31 in interest is:
P(X > 19) = = P (Z < -1.11) = 1 - P(Z ≤ -1.11)) =0.13350 = 13.35%
The proportion of the bank's Visa cardholders that paid less than 19 dollars in interest is 13.35%.
d) Let's suppose this amount of payment is Y:
Therefore P(X > Y) = 0.18
so P(X < Y) = 0.82
Utilizing standard normal approximation
P(X ≤ Y) = = P (Z ≤
) = 0.82
Form the standard normal table we find that = 0.92
Therefore,
Y - 29 = 9×0.92
Y - 29 = 8.28
Y = 8.28 + 29 = 37.28
Therefore $37.28 of interest payment is exceeded by only 18% of the bank's Visa cardholders.