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The histogram depicts the weights of quarters made before 1964 and the weights of quarters made after 1964. The pre-1964 quarters were made with 90% silver and 10% copper. The post-1964 quarters are made with a copper-nickel alloy. What is the value of each class width and how many quarters that weigh less than 5.6 grams? Is this histogram normal? Why or why not? What is a reasonable explanation for the gap between quarter with weights between 5.5 grams to 5.8 grams and the group of quarters with weights between 6 grams to 6.4 grams?

The histogram depicts the weights of quarters made before 1964 and the weights of quarters made after 1964 The pre 1964 quarters were made with

Answer :

The class width for pre-1964 quarters is 0.1 grams, and for post-1964 quarters, it is also 0.1 grams. There are 39 quarters weighing less than 5.6 grams. The histogram exhibits a gap, suggesting a non-normal distribution possibly due to changes in coin composition.

The class width is the difference between the upper and lower class boundaries. From the given histogram, we can determine the class width for both sets of quarters:

For the weights before 1964:

Class width = 5.7 - 5.6 = 0.1 grams

For the weights after 1964:

Class width = 6.1 - 6.0 = 0.1 grams

To find the total number of quarters that weigh less than 5.6 grams, we sum the frequencies of the first three classes: 12 + 19 + 8 = 39 quarters.

Regarding the normality of the histogram, it may not be considered normal. A normal distribution typically forms a bell-shaped curve, and this histogram appears to have a gap between the group of quarters with weights between 5.5 grams to 5.8 grams and the group with weights between 6 grams to 6.4 grams. A normal distribution does not have such gaps and should exhibit a smooth transition between adjacent classes.

A reasonable explanation for the gap could be a difference in the manufacturing processes or materials used. The gap may indicate a distinct separation in the weights of the quarters, possibly due to changes in the composition of the coins. For example, a shift from silver-copper alloy to copper-nickel alloy in the post-1964 quarters could explain the gap, as different materials may result in different weight distributions.

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