Question

You may need to use the appropriate appendix table or technology to answer this question. The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 35 years of rainfall for California and a sample of 46 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. inches 19.9 20.6 21.3 22 22.7 23.4 24.1. inches 39.9 40.6 413 42 42.7 43.4 44.1 stal at th sle of

Answer 1

mean μ=	22.000
standard deviation σ=	4.000
sample size       =n=	35
std error=σx̅=σ/√n=	0.6761

1st graph is correct

inches 19.9 20.6 213 22 22.7 23.4 24.1

b)

probability =

P(21<X<23)

=

P(-1.48<Z<1.48)=

0.9306-0.0694=

0.8612

c)

sample size       =n=	46
std error=σx̅=σ/√n=	0.5898

probability =

P(41<X<43)

=

P(-1.7<Z<1.7)=

0.9554-0.0446=

0.9108

d)

part c) because the sample size is larger\