Problem 3: Running Distance

A specific phone application records the distance in miles of its members' exercise runs. There are 24,112 members of this app. The data set called "Running Distance" contains each member's last recorded run distance in miles.

a)Graph the distribution of the "Distance" variable using a relative frequency histogram. Properly title and label this graph and copy it into your document.

b)Interpret the shape of the distribution of the distances of all members in one complete sentence.

c)Find the proportion of all members using this app whose last run was 5 miles or longer (assuming 5 miles is recorded in the bar to the right of the tick mark 5).You can click on the bars of your histogram to help obtain this value.You do not need to copy the highlighted histogram into your document. Show the values used for the calculation of the proportion as well as your answer.Round your proportion to four decimal places.Hint: you can obtain this proportion in a number of ways using your histogram and considering compliments.

d)Use StatCrunch to obtain the mean and standard deviation for the "Distance" variable by using Stat Summary Stats Columns.Copy the table and round the mean and standard deviation to two decimal places.Are these measures you found parameters or statistics?Answer this question in one sentence.

e)Take one sample of size 17 from the "Distance" variable using Data Sample.Once in the box, click on the column you want to sample from.Then, enter 17 for your sample size and keep the number of samples as 1.Finally click Submit. Once you have your sample, calculate the mean and standard deviation of this sample.Copy the table with the mean and standard deviation into your document and round both values to two decimal places.

f)Are these measures you found in part (e) parameters or statistics?Answer this question in one sentence.

g)Does the mean calculated in (e) come from a sampling distribution that is approximately Normal?Check all three conditions of the Central Limit Theorem using one complete sentence for each condition to answer this question.

h)Now take one sample of size 35 from the population using Data Sample and calculate the mean and standard deviation of this sample. Copy the table with the mean and standard deviation into your document and round both values to two decimal places.

i)Are these measures you found in part (h) parameters or statistics?Answer this question in one sentence.

j)Does the mean calculated in (h) come from a sampling distribution that is approximately Normal?Check all three conditions of the Central Limit Theorem using one complete sentence for each condition to answer this question.

k)Calculate the probability that, in a random sample of 35 app members, the mean distance of their last run is 5 miles or longer.

First, draw a picture with the mean and value labeled and the shaded area representing the desired probability.Please take a picture of your hand drawn sketch and upload it to your Word document (if you do not have this technology, you may use any other method (i.e. Microsoft paint) to sketch the image).

Then, complete the problem by standardizing and using the Standard Normal Table to obtain this probability.You must type the rest of your "by hand" work to earn full credit.

l)Verify your answer in part (k) using the StatCrunch Normal calculator and copy that image into your document.In addition, write one sentence to explain what the probability means in context of the question.