Question

# You work for a consumer watchdog publication and are testing the advertising claims of a tire...

You work for a consumer watchdog publication and are testing the advertising claims of a tire manufacturer. The manufacturer claims that the life spans of the tires are normally​ distributed, with a mean of​ 40,000 miles and a standard deviation of 40004000 miles. You test 16 tires and get the following life spans. Complete parts​ (a) through​ (c) below. 48,819  40,986 28,175  37,525  29,515 41,602 38,865 37,866 23,405 30,245 38,601 33,815 30,521 37,289 37,018  44,084

​(a) Draw a frequency histogram to display these data. Use five classes. Choose the correct answer below.

Is it reasonable to assume that the life spans are normally​ distributed? Why? Choose the correct answer below.

A. Yes, because the histogram is symmetric and​ bell-shaped.

B. ​Yes, because the histogram is neither symmetric nor​ bell-shaped.

C. No, because the histogram is symmetric and​ bell-shaped.

D. No, because the histogram is neither symmetric nor​ bell-shaped.

​(b) Find the mean of your sample. ​(Round to one decimal place as​ needed.)

Find the standard deviation of your sample. ​(Round to one decimal place as​ needed.)

 23,405 28,175 29,515 30,245 30,521 33,815 37,018 37,289 37,525 37,866 38,601 38,865 40,986 41,602 44,084 48,819

Range=48819-23405=25414

No. of class=5

Class width=25414/5=5082.8

so taking Class width=5100

Frequency Distribution

 Class Width Frequency 23400-28500 2 28500-33600 3 33600-38700 6 38700-43800 3 43800-48900 2

a.) Frequency Histogram

Ans: A.Yes, because the histogram is symmetric and​ bell-shaped.

b.)Mean=36146

Standard Deviation=5626.3 (using excel.)

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