The average amount of rain per year in Greenville is 49 inches. The standard deviation is 8 inches. Find the probability that next year Greenville will receive the following amount of rainfall. Assume the variable is normally distributed. A) At most 55 inches of rainB) at least 62 inches of rainC) Between 46 and 55 inches of rainD) How many inches of rain would you consider to be an extremely wet year?

The probability that next year Greenville will receive the following amount of rainfall A) At most 55 inches of rain is 0.7734, B) at least 62 inches of rain is 0.0516, C) Between 46 and 55 inches of rain is 0.0387

D Having rainfall of above 65 inches would be considered as an extremely wet year

Step-by-step explanation:

A. To find the probability that next year Greenville will receive at most 55 inches of rain we would have to make the following calculation:

P(X<55)

=P((X-mean)/s<(55-49)/8)

=P(Z<0.75)

=0.7734

The probability that next year Greenville will receive at most 55 inches of rain is 0.7734

B. To find the probability that next year Greenville will receive at most 62 inches of rain we would have to make the following calculation:

P(X>62)

=P(Z>(62-49)/8)

=P(Z>1.63)

=0.0516

The probability that next year Greenville will receive at most 62 inches of rain is 0.0516

C. To find the probability that next year Greenville will receive at Between 46 and 55 inches of rain we would have to make the following calculation:

P(46<X<54)

=P((46-49)/8 <Z<(54-49)/8)

=P(-0.38 <Z< 0.63)

=0.3837

The probability that next year Greenville will receive Between 46 and 55 inches of rain is 0.3837

D. Here consider a value that is more two standard deviations above the mean as an unusual vale. That is:

X=2σ+μ

=2(8)+49

=65

Therefore, having rainfall of above 65 inches would be considered as an extremely wet year.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560