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Question

Note: Answer the Question(s) by Using the TI-30XA (or other approved) Calculator. IMPORTANT: Make sure you carry all decimals until you reach your answer, then round to four decimals The state of California has a mean annual rainfall of 23.8 inches, whereas the state of New York has a mean annual rainfall of inches. Assume the standard deviation for California is 4.9 inches and for New York is 8.2 inches. Find the probablity for a sample of 40 years of rainfall for New York, the mean annual rainfall s at least 47 inches. (See exercise 24 on page of your textbook for a similar problem.) that, 326

Explanation / Answer

mean annual rainfall of new york state is 46.3

standard deviation of new york state 8.2

given sample size is 40

standard error for mean annual rainfall for sample size of 40 = standard deviation/n = 8.2/40 = 1.2967

z value . = (x-mean)/(standard error)

z value for 47 is (47-46.3)/1.2967 = 0.5398, corresponding p value i.e(p value for z=0.5398) using z table is 0.7053

so P(mean annual rainfall <= 47) = 0.7053

P(mean annual rainfall > 47) = 1- 0.7053 = 0.2947

so probability that for a sample of 40 years of rainfall for New York, the mean annual rainfall is at least 47 inches = 0.2947

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