SOLUTION: a) Suppose that a civil service examination is designed so that 70% of all persons with an IQ of 90 can pass it. Find the probability that among 14 persons with an IQ of 90 who tak
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Question 1156906: a) Suppose that a civil service examination is designed so that 70% of all persons with an IQ of 90 can pass it. Find the probability that among 14 persons with an IQ of 90 who take the test
i. At most 5 will pass.
ii. At least 11 will pass.
iii. From 8 through 12 will pass
You can put this solution on YOUR website! i. At most 5 will pass.
n = 14
p = 0.70
q = 0.30
MEAN = np = 14(0.70) = 9.8
SD = = = 1.7146
P(X ≤ 5) ---> P(X < 5 + 0.5) ---> P(X < 5.5)
Z = = -2.51
On a z-table, -2.51 is equal to 0.0060. That means the area to the left of the curve is 0.0060. So, the probability "at most 5 will pass" is 0.0060.
============================================================== ii. At least 11 will pass.
n = 14
p = 0.70
q = 0.30
MEAN = np = 14(0.70) = 9.8
SD = = = 1.7146
P(X ≥ 11) ---> P(X > 11 - 0.5) ---> P(X > 10.5)
Z = = 0.41
On a z-table, 0.41 is equal to 0.6591. That means the area to the right of the curve is 0.3409. So, the probability "at least 11 will pass" is 0.3409.
============================================================== iii. From 8 through 12 will pass.
n = 14
p = 0.70
q = 0.30
MEAN = np = 14(0.70) = 9.8
SD = = = 1.7146
P(8 ≤ X ≤ 12) ---> P(8 - 0.5 < X < 12 + 0.5) ---> P(7.5 < X < 12.5)
Z1 = = -1.34
Z2 = = 1.57
On a z-table:
-1.34 is equal to 0.0901
1.57 is equal to 0.9418
Simply subtract 0.0901 from 0.9418 to get a result of 0.8517. So, the probability "from 8 through 12 will pass" is 0.8517.
