The average amount or precipatiion in Dallas, Texas, during the month of april 1

Question

The average amount or precipatiion in Dallas, Texas, during the month of april 1s 3.5 inches. Assume that a normal distribution applies and that the standard deviation is .8 inches.

What percentage of the time does the amount of rainfall in April exceed 5 inches?

What percentage of time is the amount of rainfall in April less than 3 inches?

A month is classified as extremely wet if the amount of rainfall is in the upper 10% for that month. How much precipitation must fall in April for it to be classified as extrememly wet?

Explanation / Answer

1. P(X > 5)

= P(z > (3.5 - 5)/0.8)

= P(z > -1.875)

= 0.9696

2. P(X< 3)

= P(X < (3 - 3.5)/0.8)

= P(X < -0.625)

= 0.2660

3. Let precipitation that must fall in April for it to be classified as extrememly wet is k. Then,

P(X > k) = 0.1

P(z > (k - 3.5)/0.8) = 0.1

From z table,

P(z > 1.28) = 0.1

Hence,

(k - 3.5)/0.8 = 1.28

k = 3.5 + 0.8(1.28)

k = 4.524

Hence,

The precipitation must be 4.52 inches or greater.

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