The Volkswagen Type 2, informally known as the VW Bus, was first introduced in 1950.The first generation of the Type 2, which was produced until 1967, has an active aftermarket with vehicles frequently sold for high prices at auction.The dataset (called "VW Bus Auction Sales") for the winning bid of 126 unrestored VW Type 2's sold at auction are given on StatCrunch.

a)Use StatCrunch to construct an appropriately titled and labeled relative frequency histogram of the winning bid (in dollars). Copy your histogram into your document.

b)What is the shape of this distribution?Answer this question in one complete sentence.

c)Using your histogram, determine the proportion of winning bids of $75,000 or more.To do this, click on each bar that is representing $75,000 or more and look in the bottom left to see how many individual times are highlighted.Provide the image of the highlighted histogram and the correct proportion (type your work for the calculation of the proportion).

d)Now overlay your highlighted histogram from 2(c) with a normal curve and add a vertical line at the mean.

This can be done by going to Options Edit in the top left corner of your graph.Inside the histogram graph box, look for Display Options.Next to "Overlay distrib.:" click the arrow next to the word --optional-- and select Normal.Then, check the box next to mean under the word "Markers." Copy and paste this histogram into your document.

e)Do you think it is reasonable to use the normal probability model in this case?Answer this question and provide a reason why in one sentence.

f)Calculate the sample size, the mean, and the standard deviation of the "Winning Bid" variable using StatCrunch.(Select Stat Summary Stats Columns.)Copy and paste this table into your document.Round the mean and standard deviation to whole numbers inside this table.

For parts (g) - (l), assume that the distribution of winning bid prices in the population is normal with the mean and standard deviation found in part 2(f) (again use the rounded mean and standard deviation values).Note: you are using the normal distribution for the next three calculations.

g)Calculate the probability that a randomly selected winning bid is $75,000 or more.First, draw a picture with the mean labeled and shade the area representing the desired probability.Next, standardize the value and use the Standard Normal Table (Table 2 in your text) to obtain this probability.Then, take a picture of your hand drawn sketch and upload it to your document (if you do not have this technology, you may use any other method (i.e. Microsoft paint) to sketch the image into your document).You must type the rest of your "by hand" work to earn full credit.

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

i)Compare this probability to the proportion you calculated in part (c).Label each probability as a theoretical or an empirical probability in your comparison.

j)Use StatCrunch only to calculate the probability that a randomly selected winning bid is between $55,300 and $67,200.Copy the normal distribution image from StatCrunch with the values displayed into your document.Then, once you obtain your answer, write one sentence to explain what the probability means in context of the question.

k)An individual looking to obtain a VW Bus is looking for a good deal.They will only place a bid on the bus if it is within the 7.5^th percentile (i.e. the bottom 7.5%) of all winning bids.What is the maximum value that this individual is willing to bid?Draw a picture of the density curve, shade the area, and use the standard normal table to solve this problem.Take a picture of your hand drawn sketch and upload it to your document (if you do not have this technology, you may use any other method (i.e. Microsoft paint) to sketch the image).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.