1. It is generally believed that nearsightedness affects about 12% of children.

Question

1. It is generally believed that nearsightedness affects about 12% of children. A school district gives vision tests to 144 random incoming kindergarten children. What percent of such samples would you expect to have less than 15% of the children be nearsighted?

A) 90.78%

B) 15%

C) 12%

D) 9.22%

2. It is known that 76% of all cars on the interstate exceed the speed limit. What is the probability that more than 400 out of a random sample of 500 cars exceed the speed limit on the interstate?

A) 0.0000

B) 0.0183

C) 0.0073

D) 0.0127

Explanation / Answer

1) Option A
p = 0.15
pcap = 0.12 , n =144
se = sqrt(p*(1-p)/n)
= sqrt((0.15 * 0.85)/144)
= 0.0298

P(p < 0.15)

z = (0.15 - 0.12)/SE
= ( 0.15 -0.12)/0.0298
= 1.0067

P(p < 0.15) = P(z < 1.0067) = 0.843 = 84.3%

Option A approximately matches with 84.35

2)
n = 500 , p = 0.76

mean = np = 0.76 * 500 = 380

std.deviation = sqrt(npq)
= sqrt(0.76 * 500 * 0.24)
= 9.5499

P(x > 400)

z = ( 400 - 380)/9.5499
= 2.0943

P(x > 400) = P(z > 2.0943) = 0.0181

Option B) is correct

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