5.7 After the spring season, the water level of a lake in feet, X, has a near no

Question

5.7 After the spring season, the water level of a lake in feet, X, has a near normal distribution with mean 1875 and standard deviation 1.5. Using the normal probability rule, approximate

(a) P[1872 < X < 1878].

(b) P[X 1879.5].

5.8 Let X be a binomial random variable with n=20 and p = 0.6, i.e., X~B(20,0.6).

(a) Is the normal approximation appropriate for X? Whatever your answer in(a), solve (b) and (c).

(b) Compare the exact and approximate values for P[X = 10].

(c) Compare the exact and approximate values for P[7 X 10].

Explanation / Answer

5.7 After the spring season, the water level of a lake in feet, X, has a near normal distribution with mean 1875 and standard deviation 1.5. Using the normal probability rule, approximate
(a) P[1872 < X < 1878].

Note that 1872 and 1878 are 2 standard deviation below and above the mean, respectively.

Hence, by 68-95-99.7 rule, it makes up 95%. [ANSWER: 95%]

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(b) P[X 1879.5].

Note that 1879.5 is 3 standard deviations above the mean.

Hence, those above it make up (100-99.7)/2 = 0.15% [ANSWER, 0.15%]

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