Question

The last group of problems will use daily high temperature data for Santa Fe,
New Mexico during the month of May. For the sake of the assignment, we will
assume that the dataset is normally distributed. The only information you’ll need
are the standard deviation (7.92) and the mean (84.31).
1a. Before we dive into the problems, think a little bit about the normal distribution (and
the normal curve). What are you really finding when you find the probability of a range

of high temperatures?

1b. How does this relate to your ability to find the probability of a single temperature of

90 degrees F?

1c. Draw the normal curve and label the mean, median and mode. Also label where your

z-score would equal 0, +3 and -3.

1d. What is a z-score?

Answer 1

Hello Sir/ Mam

Given that :

Mean = 84.31 and Standard Deviation = 7.92

1a) When we find the probability of a range of temperatures, we are really finding the difference of the probabilities of an obtaining value less than upper range and obtaining value less than lower range, i.e.

If we want to find the P( a < X < b ), then, in fact first we find the z-scores for both a and b and then we find their difference and we write iti as :

P(z < b) - P(z < a)

1b) With reference to the above, if we find the probability of a single temperature, it will comes out to be zero. This indicated that the probability of a single point or a single value in the normal distribution is approximately equal to zero.

1c)

1d) z - score is a value of given X of a normal distribution in a similar standard normal distribution. We can also say that z - score is a mirror image of X( which we want to analyse/ for which we are to calculate probability).

I hope this solves your doubt.

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