Question

(a) Sketch a possible graph of the distribution of sample data for an SRS of size $5$ with a range of $1000$grams.

(b) Explain why the dotplot of sample ranges above is not the actual sampling distribution of the sample range.

Short answer

(a)

(b)The range of both the distributions is not equal because the provided data plot has the range of $500$samples while the actual one has the sample range for all the samples of $500$size.

Step-by-step solution

Part(a) Step 1: Given information

Given in the question that, Researchers in Norway analyzed data on the birth weights of $400,000$newborns over a six-year period. The distribution of birth weights is approximately Normal with a mean of $3668$grams and a standard deviation of $511$gra ms. I$9$n this population, the range (maximum – minimum) of birth weights is$3417$grams. We used Fathom software to take $500$SRSs of size $n=5$and calculate the range (maximum – minimum) for each sample. The dotplot below shows the results.

• We need to draw Sketch a possible graph of the distribution of sample data for an SRS of size $5$with a range of $1000$grams.

Part(a) Step 2: Explanation

Given,

Figure is,

Consider, the numbers are $2800,3000,3200,3400,3800.$

The figure could be constructed as:

Part(b) Step 1: Given information

Researchers in Norway analyzed data on the birth weights of $400,000$newborns over a six-year period. The distribution of birth weights is approximately Normal with a mean of $3668$grams and a standard deviation of$511$grams.$9$In this population, the range (maximum – minimum) of birth weights is $3417$grams. We used Fathom software to take $500$SRSs of size$n=5$and calculate the range (maximum – minimum) for each sample. The dotplot below shows the results

Part(b) Step 2: Explanation

The range of both the distributions is not equal because the provided data plot has the range of $500$ samples while the actual one has the sample range for all the samples of $500$ size.