1. The state of California has a mean annual rainfall of 27.6 inches, whereas th

Question

1. The state of California has a mean annual rainfall of 27.6 inches, whereas the state of New York has a mean annual rainfall of 44.5 inches. Assume the standard deviation for California is 4.9 inches and for New York is 3.1 inches. Find the probability that, for a sample of 45 years of rainfall for California, the mean annual rainfall is at least 29 inches.

2. The Better Business Bureau settles 85% of complaints it receives involving new car dealers. Suppose a sample of 120 complaints involving new car dealers is selected. Find the probability that Better Business Bureau settles less than 105 of these complaints.

**Carry all decimals until you reach your answer, then round to four decimals.**

Explanation / Answer

1)

mean = 27.6 , s = 4.9 , n = 45

P(x > 29)
z = ( x - mean) / (s/sqrt(n))
= ( 29 - 27.6) / ( 4.9/sqrt(45))
= 1.916
we need to find P(z > 1.916) by using z standard right tail, we get ,

P(x > 29) = P(z > 1.916) = 0.0276

2)

P = 0.85 , n = 120 , p = 105 / 120 = 0.87

P(p < 0.87)

z = ( p - P) / sqrt( P ( 1 -p) / n)
= ( 0.87 - 0.85) / ( 0.85 * 0.15 / 120)
= 0.6135
we need to find P(z <0.6135) by using z standard right tail, we get ,

P(x < 0.87) = P(z < 0.6135) = 0.734

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