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This is a question on normal distribution . Please provide a detailed explanation on this. Thanks in advance!
![14 Once a week, Haziq rows his boat from the island where he lives to the mainland. The journey time,
X minutes, is normally distributed with mean u and variance o?.
a Given that P(20 < X < 30) = 0.32 and that P(X < 20) = 0.63, find the values of µ and oʻ.
b The time taken for Haziq to row back home, Y minutes, is normally distributed and P(Y < 20) = 0.6532.
Given that the variances of X and Y are equal, calculate:
i
the mean time taken by Haziq to row back home
ii the expected number of days over a period of five years (each of 52 weeks) on which Haziq takes more
than 25 minutes to row back home.](https://content.bartleby.com/qna-images/question/dcd04ba4-8061-4bb9-9367-f0aab1a3c8dd/a0e3a30c-a16a-4263-8925-83d3bd196c4e/o5jb1sd_thumbnail.jpeg)
Transcribed Image Text:14 Once a week, Haziq rows his boat from the island where he lives to the mainland. The journey time,
X minutes, is normally distributed with mean u and variance o?.
a Given that P(20 < X < 30) = 0.32 and that P(X < 20) = 0.63, find the values of µ and oʻ.
b The time taken for Haziq to row back home, Y minutes, is normally distributed and P(Y < 20) = 0.6532.
Given that the variances of X and Y are equal, calculate:
i
the mean time taken by Haziq to row back home
ii the expected number of days over a period of five years (each of 52 weeks) on which Haziq takes more
than 25 minutes to row back home.
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