Nine percent of men and 0.25% of women cannot distinguish between the colors red

ID: 3039912 • Letter: N

Question

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. In a sample of 15 men, let X be the number who are color blind. Consider the following probability distribution for X.

(b) Suppose that a group of 15 men are randomly selected, and 3 of them are color blind. Is this a significantly high number that would suggest that the given percentage of men that are color blind (i.e., 9%) is not correct?

(A) Yes, because 0.1468 is greater than .05. (B) Yes, because 0.2496 is greater than .05. (C) Yes, because 0.107 is greater than .05. (D) Yes, because 3 a lot more than expected. (E) No, because 0.2496 is greater than .05. (F) No, because 3 a not a lot more than expected. (G) No, because 0.1468 is greater than .05. (H) No, because 0.107 is greater than .05.

x P(x) 0 ? 1 ? 2 a 3 0.1070 4 0.0317 5 0.0069 6 0.0011 7 0.0001 8 0.0000 9 0.0000 10 0.0000 11 0.0000 12 0.0000 13 0.0000 14 0.0000 15 0.0000
(a) Find the missing entry that is labelled as 'a'.

Explanation / Answer

Ans:

a)Binomial distribution:

P(x=r)=15Cr*0.09r*(1-0.09)15-r

P(x=2)=15C2*0.092*0.9113=0.2496

b)P(x=3)=0.107 i.e. >0.05

Yes, because 0.107 is greater than .05.

Option C is correct.

x p(x) 0 0.2430 1 0.3605 2 0.2496 3 0.1070 4 0.0317 5 0.0069 6 0.0011 7 0.0001 8 0.0000 9 0.0000 10 0.0000 11 0.0000 12 0.0000 13 0.0000 14 0.0000 15 0.0000

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Nine percent of men and 0.25% of women cannot distinguish between the colors red

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