Carly commutes to work, and her commute time is dependent on the weather. When the weather is good, the distribution of her commute time is approximately normal with mean 20 minutes and standard deviation 2 minutes. When the weather is not good, the distribution of her commute times is approximately normal with mean 30 minutes and standard deviation 4 minutes. Suppose the probability that the weather will be good tomorrow is 0.9. What is the probability that Carly's commute time tomorrow will be greater than 25 minutes?

Question

Glenn Beasley

Mathematics

15 July, 04:55

Carly commutes to work, and her commute time is dependent on the weather. When the weather is good, the distribution of her commute time is approximately normal with mean 20 minutes and standard deviation 2 minutes. When the weather is not good, the distribution of her commute times is approximately normal with mean 30 minutes and standard deviation 4 minutes. Suppose the probability that the weather will be good tomorrow is 0.9. What is the probability that Carly's commute time tomorrow will be greater than 25 minutes?

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Paulina Bray · Answer 1

We are given with

x1 = 20 min

s1 = 2 min

x2 = 30 min

s2 = 4 min

p = 0.9

Condition (x > 25)

We need to get the t-value between the two means and comparing it wit the t-value for the time of 25 minutes given that there is a 90% probability that the weather will be good. Simply use the t-test formula and use the t-test table to get the probability.