Question

1. The probability of a man not hitting the target at a shooting range is .6. A success is defined as hitting the target. If he shoots 12 times, what is the probability that he misses the target just once?

2. The probability of a man not hitting the target at a shooting range is .6. A success is defined as hitting the target. If he shoots 12 times, what is the probability that he does hit the target at most 3 times?

3. Nine percent of all men cannot distinguish between the colors red and green.This is the type of color blindness that causes problems with traffic signals. Let the random variable X represent the number of men with red/green color blindness and let success be defined as a man being red/green color blind. If
six men are randomly selected for a study of traffic signal perceptions, what is the standard deviation of the random variable X? (round the answer to the tenths place) ____

Answer 1

1)

Here, n = 12, p = 0.6, (1 - p) = 0.4 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 1)
P(X = 1) = 12C1 * 0.6^1 * 0.4^11
P(X = 1) = 0.0003

2)

Here, n = 12, p = 0.4, (1 - p) = 0.6 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 3).
P(X <= 3) = (12C0 * 0.4^0 * 0.6^12) + (12C1 * 0.4^1 * 0.6^11) + (12C2 * 0.4^2 * 0.6^10) + (12C3 * 0.4^3 * 0.6^9)
P(X <= 3) = 0.0022 + 0.0174 + 0.0639 + 0.1419
P(X <= 3) = 0.2254

3)

p = 0.09 , n = 6

std.deviation = sqrt(npq)
= sqrt(6 *0.09 * 0.91)
= 0.7