Assume that X has a normal distribution and find the indicat

Assume that X has a normal distribution, and find the indicated probability. 13) The mean is a mu = 60.0 and the standard deviation is a sigma = 4.0. Find the probability that X is less than 53.0. A) 0.0802 B) 0.0401 C) 0.5589 D) 0.9599 Solve the problem. 14) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 89 inches, and a standard deviation of 14 inches. What is the probability that the mean annual snowfall during 49 randomly picked years will exceed 91.8 inch? A) 0.0026 B) 0.0808 C) 0.5808 D) 0.4192

Solution

13.
population mean,u = 60
standard deviation,sigma = 4

P(X< 53 ) = P(Z< ((53-60) / 4)
= P(Z< -1.75 )
= 1 - P(Z<1.75)
= 1 - 0.9599
= 0.0401

[To find P(Z<1.75) look in the standard normal table in the row 1.70 and column 0.05 (1.75 = 1.70 + 0.05), the value obtained is 0.9599]

14.
population mean,u = 89
standard deviation,sigma = 14
sample size,n = 49

standard error = sigma/sqrt(n) = 2

P(X> 91.8 ) = P(Z> ((91.8-89) / 2)
= P(Z> 1.40 )
= 1 - P(Z<1.4)
= 1 - 0.9192
= 0.0808