Question

8. The daily high temperatures for April are normally distributed with a mean of 68.7º and a standard deviation of 4.5 X = 르 a. What is the probability that in a sample of 10 randomly selected days the average high temperature is more than 65°? nl b. What is the probability that on a randomly selected day the high temperature would be between 75* and 80%?

Answer 1

Given :

The daily high temperatures for April are normally distributed with a mean of 68.7 and a standard deviation of 4.5.

Mean = $\mu$ = 68.7

Standard deviation = $\sigma$ = 4.5

Let X be the daily high temperatures for April.

Therefore

XN Normal (I= 68.710=4.5) abn = 10 P(X) 6 5) - J-P674 6 ) FI-P(Zull 65-68.7 ols 4.51510 F1-P(Z <-2160) -1-0-00466 0.9953 PC 2 PIX>65) -10.9953 a o 1 b> P(954X280) = P(752028074) FP/75-68.7 cze 80 80-68.47 -p(1.4<<<2.51) -P(Z <2.51) - P(Z <1.4) 0.99396~0.91924 4.5 4.5 11 0.0747

a) Theprobability that in a sample of 10 randomly selected days the average high temperature is more than 65 is 0.9953 nl

b) The probability that on a randomly selected day
the high temperature would be between 75 and 80 is 0.0747 nl