Question

1. determine whether the data modeled in the histogram is normally distributed (yes) or not (no).

a. yes
b. no

Explanation:

A normal distribution (bell - shaped curve) has the highest frequency in the middle and frequencies tapering off symmetrically on both sides. In the given histogram for U.S. Employment (Ages 40 - 74), the frequencies increase up to a peak (around 50 - 54 age group) and then decrease as age increases. But the left - hand side (lower age groups: 40 - 44, 45 - 49) and the right - hand side (higher age groups: 65 - 69, 70 - 74) do not show a symmetric tapering. However, wait, actually, let's re - evaluate. Wait, the normal distribution is symmetric about the mean. But in this histogram, the peak is around the middle age groups (50 - 54), and then as we move to lower ages (40 - 44, 45 - 49) the frequencies are almost equal to the peak, and then as we move to higher ages (55 - 59, 60 - 64, etc.) they decrease. Wait, no, actually, the key is that a normal distribution should have the data symmetric around the mean, with most data near the mean and tapering off equally on both sides. But in this case, the left side (lower ages) has frequencies that are high and then the right side (higher ages) has frequencies that decrease. Wait, maybe I made a mistake. Wait, the histogram for age - related employment: typically, employment rates for ages 40 - 74: the number of employed people increases up to a certain age (like 50 - 54) and then decreases as people approach retirement. But a normal distribution is symmetric. However, in this histogram, the bars on the left (40 - 44, 45 - 49, 50 - 54) are relatively high, and then from 55 - 59 onwards, they start to decrease, and the right - most bars (65 - 69, 70 - 74) are much lower. But is this symmetric? Wait, no, but wait, maybe the question is considering that the data has a single peak and is roughly symmetric? Wait, no, actually, the correct approach: a normal distribution's histogram should be roughly bell - shaped, symmetric about the center. In this case, the peak is around 50 - 54, and the left side (40 - 44, 45 - 49) are almost as high as the peak, and then the right side (55 - 59, 60 - 64, 65 - 69, 70 - 74) decrease. Wait, maybe the answer is No? Wait, no, wait, let's think again. Wait, the normal distribution is symmetric, so the left and right of the peak should mirror each other. In this histogram, the left side (40 - 44, 45 - 49, 50 - 54) and the right side (55 - 59, 60 - 64, 65 - 69, 70 - 74) do not mirror. For example, the 40 - 44 and 45 - 49 bars are almost as high as 50 - 54, but on the right, 55 - 59 is lower than 50 - 54, and then each subsequent bar is lower. So the distribution is not symmetric, so it's not a normal distribution? Wait, no, wait, maybe I'm wrong. Wait, the question is about whether the data is normally distributed. A normal distribution has a single peak, is symmetric, and tapers off on both sides. In this histogram, the data has a single peak, and as we move away from the peak (50 - 54) towards lower ages (left) and higher ages (right), the frequencies decrease. Wait, the left side: 40 - 44, 45 - 49, 50 - 54: the frequencies are increasing? Wait, no, the first bar (40 - 44) is around 15, 45 - 49 is around 15, 50 - 54 is around 15, then 55 - 59 is around 13, 60 - 64 around 9, 65 - 69 around 4, 70 - 74 around 1. Wait, so the left side (40 - 54) has relatively high and stable frequencies, and the right side (55 - 74) has decreasing frequencies. So it's not symmetric, so the data is not normally distributed. So the answer is B. No.

Answer:

B. No