Question

A town’s December high temperatures average 46 ^oF with a standard deviation of 9 ^oF, while in June the mean height temperature is 75 ^oF with a standard deviation of 8 ^oF. In which month is it more unusual to have a high temperature of 64 ^oF?

	a.	June because the z-score is farther away from zero than for December
	b.	June because the z-score is closer to zero than for December.
	c.	December because the z-score is closer to zero than for June.
	d.	December because the z-score is farther away from zero than for June.

Answer 1

solution:

Let X be the ranom representing temperature in a town

i) Given that In the month of december

Mean = = 46

Standard Deviation = = 9

For 64 oF

z-score is z1 =

=

= 2

Here,Probability that in december has 64 (or) more degrees = P(z>=2)

= 1- P(z<=2)

= 1- 0.9772 [ use normal distribution table ]  

= 0.0228

i) Given that In the month of June

Mean = = 75

Standard Deviation = = 8

For 64 oF

z-score is z1 =

=

= -1.375

Here,Probability that in december has 64 (or) more degrees = P(z>=-1.375)

= P(z<=1.375)

= 0.9154 [ use normal distribution table ]  

= 0.9154

Here December has more unusual to have high temperature of 64. since ,Observe that In december P(64 (or) more degrees ) < 0.05 and it's z-score (2) is farther away from zero than for june (-1.375)

Therefore, Option-D is correct