Question

A) 3.10 Heights of 10 year olds: Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches.

What is the probability that a randomly chosen 10 year old is between 60 and 65 inches?
(please round to four decimal places)

B) In analyzing hits by bombs in a past war, a city was subdivided into 617 regions, each with an area of 0.5-mi². A total of 475 bombs hit the combined area of 617 regions. The Poisson distribution applies because we are dealing with the occurrences of an event (bomb hits) over some interval (a region with area of 0.5-mi².

a) Find the mean number of hits per region:
mean =

b) Find the standard deviation of hits per region:
standard deviation =

c) If a region is randomly selected, find the probability that it was hit exactly twice.
(Report answer accurate to 4 decimal places.)
P(X = 2) =

d) Based on the probability found above, how many of the 617 regions are expected to be hit exactly twice?
(Round answer to a whole number.)
ans =

e) If a region is randomly selected, find the probability that it was hit at most twice.
(Report answer accurate to 4 decimal places.)
P(X ≤ 2) =

Answer 1