Question

In each case below, a histogram is described. Which of these histograms should look like a bell-shaped curve because of the Central Limit Theorem: The lifetimes of 1000 batteries are recorded and plotted in a histogram. The weights of 200 animals in a zoo are recorded and plotted in a histogram. 100 students each roll a die 30 times and average the 30 numbers that they got. They plot the 100 averages in a histogram. For 60 days, someone records the number of Monarch butterflies they see each day and plots the 60 values in a histogram.

Please answer the question if you're 100% sure.

Answer 1

1) The distribution of the lifetimes of 1000 batteries are recorded and plotted in a histogram is exponetial distribution and it is skewed distribution .hence histogram of this data can't be bell shaped.

2)The distribution of weights of 200 amnimals in a zoo are recorded and it is clread that the distribution of weights will be normal distribution and therefore histogram will be of bell shaped .

3) if we have 100 students of each roll of die 30 times and we take average of 30 numbers each time. then we plot histogram for average value then resulting histogram willl be bell shhaped because according to central limit theorem the distribution of average will be normal.

4) here we dont have any evidence that most of value of number of Monarch butteflies cluster arround the central position (30th day) and it may be skewed or uniformly distributed over the 60 days therefore histogram of this data cant be bell shaped .