Answers
a.
p = 38/75 = 0.5067
b.
n = 5
x = 3
P(x) = nCx * (p^x) * ((1-p)^(n-x))
probability that exactly 3 would draw the nickel too small is
P(3) = 5C3 * (0.5067^3) * (0.4933^2)
P(3) = 10 * (0.5067^3) * (0.4933^2)
= 0.3166
c.
probability that at least one would draw the nickel too small is
P(X>=1) = 1 - P(0)
= 1 - (5C0 * 0.5067^0 * 0.4933^5)
= 1 - (1 * 0.5067^0 * 0.4933^5)
= 0.9708
d.
n = 100
p = 0.5067
using binomial approximation
mean = np = 50.67
standard deviation = sqrt(np(1-p)) = sqrt(50.67*(1-0.5067)) = 5
It would be unusual if the probability is less than 0.05
P(X>k) = 0.05
P(X
Since 0.95 = P(Z<1.645)
(k-50.67)/5 = 1.645
k = 58.895
it would be unusual if more than 58 drew the nickel too small.
a) Proportion Low Income Too Large = (28/75)*100 = 37.3%
b) Proportion High Income Too Large = (8/75) *100 = 10.7%
c) Proportion All Children Too Large = (36/75) * 100 = 48.0%
d) Conditional Probability = (28/75)/(36/75) = 0.778 (77.8%)
The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table:
Too Small Too Large Total
Low Income 12 28 40
High Income 27 8 35
Total 39 36 75
Based on this data: (give your answers as fractions, or decimals to at least 3 decimal places)
a) The proportion of children from the low income group that drew the nickel too large is:
b) The proportion of children from the high income group that drew the nickel too large is:
c) The proportion of all children that drew the nickel too large is:
d) If a child is picked at random, what is the probability they are in the low income group, given they drew the nickel too large?
answer
a) Proportion Low Income Too Large = (28/75)*100 = 37.3%
b) Proportion High Income Too Large = (8/75) *100 = 10.7%
c) Proportion All Children Too Large = (36/75) * 100 = 48.0%
d) Conditional Probability = (28/75)/(36/75) = 0.778 (77.8%)
a) Proportion Low Income Too Large = (28/75)*100 = 37.3%
b) Proportion High Income Too Large = (8/75) *100 = 10.7%
c) Proportion All Children Too Large = (36/75) * 100 = 48.0%
d) Conditional Probability = (28/75)/(36/75) = 0.778 (77.8%)