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
b 45–50	1
c 51–56	7
d 57–62	10
e 63–68	7
f 69–74	2
g 75–80	3

choose the correct histogram below

• a. histogram image
• b. histogram image
• c. histogram image
• d. histogram image

Explanation:

Step1: Recall Normal Distribution Shape

A normal distribution has a bell - shaped curve, meaning frequencies start low, increase to a peak, then decrease symmetrically.

Step2: Analyze the Frequency Distribution

• Class A (39 - 44): Frequency = 1
• Class B (45 - 50): Frequency = 1
• Class C (51 - 56): Frequency = 7
• Class D (57 - 62): Frequency = 10 (peak)
• Class E (63 - 68): Frequency = 7
• Class F (69 - 74): Frequency = 2
• Class G (75 - 80): Frequency = 3

The frequencies increase from A to D (peak at D) and then decrease from D to G. The left - hand side (classes A - C) and right - hand side (classes E - G) show a roughly symmetric pattern around the peak (class D).

Step3: Evaluate the Histogram Options

We need to find a histogram where the bar heights (frequencies) match the pattern: low frequencies for the first two classes, increasing to a peak at class D, then decreasing, with symmetry around the peak. From the given options, the histogram that shows this bell - shaped (approximately normal) pattern is the one that has the bar heights corresponding to the frequencies: short bars for A and B, taller bars increasing to D, then decreasing bars for E, F, G with a roughly symmetric shape around D.

Answer:

To determine the correct histogram and if the data is approximately normal:

1. Histogram Selection: The correct histogram should have bar heights corresponding to the frequencies: Class A (1), B (1), C (7), D (10), E (7), F (2), G (3). The histogram that shows a bell - shaped (increasing then decreasing symmetrically around the peak at D) pattern is the appropriate one (among the given options, the one with the bar heights matching the frequency distribution as analyzed).

1. Normal Distribution Check: The data appears to have a distribution that is approximately normal because the frequencies start low, increase to a single peak (at class D: 57 - 62), and then decrease, with the left - hand side (lower temperature classes) and right - hand side (higher temperature classes) of the peak showing a roughly symmetric pattern of frequencies.

For the histogram choice, based on the frequency distribution and the normal - like pattern, the correct histogram (among the options A, B, C, D) is the one that represents the frequencies as a bell - shaped curve. If we assume that option A (the one selected initially) has the correct bar heights, then the correct histogram is A, and the data is approximately normal.