Question

The 70-year long-term record for weather shows that for New York State, the annual precipitation has a mean of 39.63 inches and a standard leviation of 4.56 inches. The annual precipitation amount has a normal distribution. (Give your answers correct to four decimal places.) (a) What is the probability that next year the total precipitation for New York State is more than 50.6 inches? 0.9919 x (b) What is the probability that next year the total precipitation for New York State is between 41.6 and 48.1 Inches? 0.3012 (c) What is the probability that next year the total precipitation for New York State is between 29.9 and 37.8 inches? 0.3277 (d) What is the probability that next year the total precipitation for New York State is more than 35.6 inches? 0.1884 (e) What is the probability that next year the total precipitation for New York State is less than 45.6 inches? 0.9048 (f) What is the probability that next year the total precipitation for New York State is less than 31.8 inches? 0 0430

Answer 1

denote the Here, let precipitation x for annual New york state the Clearly x follows normal distribution with mean 39.63 inches and standard deviation 4.56 inches XN NI 39.63, 4.56 (0) The probability that next year precipitations be more than than 50.6 P (x > 50-6 Р Z 50-6-39.63 4.56 P z > 2.40590 > 8.40570) z 0.0081 41.6 L xE 48.1 48-1] 2 b] PC P 41.6- 29.63 22² 45.2-29.63 4.56 4.56 zp(0.4320 1 22 1.8573 0:3012 PL 29.9 € x 5 31.8 1-8] pe (2010 =P [-2.1358 € 25-0.4013] > P 29.9 - 39.63 4.56 € 2€37.4 - 39.63 4.5.

0.327) dll p[ X 735.6] Z 7 - 35.6 - 39.63 4.56 P[? P{ 77-0.6034] N O.8116 e plx. 45.6] plz 21.3090] 09048 f] p[xL 31.8] = = P[ 22-1.3171 0.0430 z Here, And the is the standard normal randons variable. Area is oblained by by using using ealeulators: