2. Climate change and the weather impacts of climate change are of great concern

Question

2. Climate change and the weather impacts of climate change are of great concern today. You read that the diameter of hail in the 1990s that would hit the ground in a storm had a mean diameter of 5 inch with a standard deviation of.1 inch. A fairly large hail storm hits Cleveland and you decide to see if hail is becoming significantly larger. You measure a hailstone and find it has a diameter of .71 inches. What is the percentage of hail that would have a diameter of .71 or greater based on the 1990s data?

Explanation / Answer

#2.
mean = 0.5
std. dev. = 0.1

P(X > 0.71)
= P(z > (0.71 - 0.5)/0.1)
= P(z > 2.1)
= 0.0179 (using standard normal z table)

Hence only 1.79% of hail that would have a diameter of 0.71 or greater

#3.
mean = 7
std. dev. = 2

a)
P(X < 5)
= P(z < (5 - 7)/2)
= P(z < -1)
= 0.1587 (using standard normal z table)

hence 15.87%

b)
P(X > 10)
= P(z > (10 - 7)/2)
= P(z > 1.5)
= 0.0668 (using standard normal z table)

c)
using standard z table the value of z for top 25% is 0.6745

xbar = 7 + 0.6745*2 = 8.349

Hence 8.4 is the value that seperates the top 25% response

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