Assume the lengths of cracks in the outer wall of the Swan Building are normally
ID: 3316345 • Letter: A
Question
Assume the lengths of cracks in the outer wall of the Swan Building are normally distributed, with a mean length of 28 inches and a standard deviation of 2 inches. A crack is selected at random, to answer the following: 2. a- Probability of the crack measuring less than 26 inches? b- Probability of the crack measuring between 25 and 31 inches? c- Probability of the crack measuring more than 30 inches? d- Probability of the crack measuring exactly 29 inches? e- How long do you expect the longest 11% of cracks on the building would measure?Explanation / Answer
Length of carcks are normally distributed with mean = 28 and standard deviation = 2
Let X be the length of cracks.
X ~ N(28, 4)
(a)
Probability of carck measuring less than 26
= P(X < 26)
= pnorm(26, mean = 28, sd = 2)
= 0.1586553
(b)
Probability of crack measuring between 25 and 31 inches
= P(25 < X < 31)
= P(X < 31) - P(X < 25)
= pnorm(31, mean = 28, sd = 2) - pnorm(25, mean = 28, sd = 2)
= 0.8663856
(c)
Probability of crack measuring more than 30
= P(X > 30)
= 1 - P(X <= 30)
= 1 - pnorm(30, mean = 28, sd = 2)
= 0.1586553
(d)
Probability of crack measuring exactly 29 inches
= P(X = 29)
= 0
since probability of crack measuring exactly equal to some fixed length = 0
(e)
The length of the longest 11% cracks would be equal to y
such that
P(X > y) = 0.11
=> P(X <= y) = 0.89
=> y = qnorm(0.89, mean = 28, sd = 2)
= 30.45306 inches
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