Question

the frequency distribution below represents frequencies of actual low temperatures recorded during the course of a 31 - day month. use the frequency distribution to construct a histogram. do the data appear to have a distribution that is approximately normal?
class frequency
a 39 - 44 1
b 45 - 50 1
c 51 - 56 7
d 57 - 62 11
e 63 - 68 5
f 69 - 74 3
g 75 - 80 3
choose the correct histogram below
do the data appear to have a distribution that is approximately normal?
a. no, it is approximately uniform
b. no, it is completely erratic
c. no, it is not at all symmetric
d. yes, it is approximately normal

Explanation:

Step1: Analyze the frequencies for histogram

The class - frequency pairs are: A (39 - 44) with frequency 1, B (45 - 50) with frequency 1, C (51 - 56) with frequency 7, D (57 - 62) with frequency 11, E (63 - 68) with frequency 5, F (69 - 74) with frequency 3, G (75 - 80) with frequency 3.

Step2: Match with histogram options

We look for a histogram where the bar - heights match the given frequencies in order of the classes A - G. Option D has bar - heights that match the frequencies 1, 1, 7, 11, 5, 3, 3 for classes A - G respectively.

Step3: Check for normal distribution

A normal distribution is symmetric about the mean. The frequencies here are not symmetric. The left - hand side (classes A and B) has low frequencies, then it peaks at class D and then the frequencies on the right - hand side (classes E, F, G) gradually decrease but the distribution is not symmetric. So it is not approximately normal.

Answer:

Choose the correct histogram below: D.
Do the data appear to have a distribution that is approximately normal? C. No, it is not at all symmetric.