SOLUTION: Nine percent of men and 0.25% of women cannot distinguish between the colors red and green. This is the type of color blindness that causes problems with traffic signals. (a) If

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Question 1066757: Nine percent of men and 0.25% of women cannot distinguish between the colors red and green. This is the type of color blindness that causes problems with traffic signals.
(a) If 13 men are randomly selected for a study of traffic signal perceptions, find the probability that between 1 and 3 inclusive of them have this type of color blindness.
(b) In a group of 230 men, find the mean number that are color blind.
(c) In a group of 230 men, find the standard deviation of the number that are color blind.
(d) Suppose that a group of 230 men are randomly selected, and 31 of them are color blind. Is this an unusual result that would perhaps suggest that the given percentage of men that are color blind (i.e., 9%) is not correct?
Answer by stanbon(75887) About Me  (Show Source):
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Nine percent of men and 0.25% of women cannot distinguish between the colors red and green. This is the type of color blindness that causes problems with traffic signals.
(a) If 13 men are randomly selected for a study of traffic signal perceptions, find the probability that between 1 and 3 inclusive of them have this type of color blindness.
P(x = 1) = 13C1(0.09)*(0.91)^12 = binompdf(13,0.09,1) = 0.3773
P(x = 2) = binompdf(13,0.09,2) = 0.2239
P(x = 3) = binompdf(13,0.09,3) = 0.0812
Ans:: Add to get:: 0.68
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(b) In a group of 230 men, find the mean number that are color blind.
Ans: mean = n*p = 230*0.09 = 20.7
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(c) In a group of 230 men, find the standard deviation of the number that are color blind.
std = sqrt(npq) = sqrt(20.7*0.91) = 4.34
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(d) Suppose that a group of 230 men are randomly selected, and 31 of them are color blind. Is this an unusual result that would perhaps suggest that the given percentage of men that are color blind (i.e., 9%) is not correct?
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z(31) = (31-20.7)/4.34 = 2.37
31 is 2.37 standard deviations above the mean.
Based on that result you might question the 9% standard for men.
Cheers,
Stan H.
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