THIS QUESTION REQUIRES GREAT KNOWLEDGE OF THE SOFTWARE R STUDIOS (CODE) AND STAT

Question

THIS QUESTION REQUIRES GREAT KNOWLEDGE OF THE SOFTWARE R STUDIOS (CODE) AND STATISTICS

Question 5. If commuting times are normally distributed with mean 25.4 minutes, and standard deviation is 12.1 minutes.

A- What is the probability that a commuting time is shorter than 26.0 minutes. Calculate by hand and by R.

B- What is the probability that a commuting time is longer than 35 minutes. Calculate by hand and by R, and attach the R code and the result in your homework.

" PLEASE PASTE THE R STUDIOS CODE USED FOR ANSWERING BOTH QUESTION"

Explanation / Answer

a) mean = 25.4, s = 12.1, x = 26
P(X < 26) = P(Z < (X-mean)/s) = P(Z < (26-25.4)/12.1) = P(Z < 0.04959) = 0.5198

R code:
pnorm(26, 25.4, 12.1,lower.tail = TRUE)
[1] 0.5197742

b) P(X > 35) = P(Z > (X-mean)/s) = P(Z > (35-25.4)/12.1) = P(Z > 0.79339) = 0.2138

R code:
pnorm(35, 25.4, 12.1,lower.tail = FALSE)
[1] 0.2137758

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