You have arranged to go camping for two days in March.You believe that the probability that it will rain on the first day is 0.4.If it rains on the first day,the probability that it also rains on the second day is 0.5.If it doesn't rain on the first day,the probability that it rains on the second day is 0.3.Let the random variable X be the number of rainy days during your camping trip.Find the standard deviation of X.
A)σ = 0.67
B)σ = 0.76
C)σ = 0.57
D)σ = 0.77
E)σ = 0.70

Question

Quizplus · Accepted Answer

To find the standard deviation of X, we first need to find the expected value of X, which is E(X) = np, where n is the number of days (2) and p is the probability of rain on any given day.

For the first day, the probability of rain is 0.4, so the probability of no rain is 0.6. Thus, the probability of rain on both days is (0.4)(0.5) = 0.2, the probability of rain on the second day only is (0.6)(0.3) = 0.18, the probability of rain on the first day only is (0.6)(0.5) = 0.3, and the probability of no rain on both days is (0.6)(0.7) = 0.42.

Therefore, the expected value of X is E(X) = (2)(0.4) = 0.8.

To find the standard deviation of X, we use the formula σ = sqrt(np(1-p)). Plugging in values, we get: 
σ = sqrt(2*0.4*0.6) = 0.774

Therefore, the answer is B with a standard deviation of 0.77.

You Have Arranged to Go Camping for Two Days in March.You