Many automotive experts believe that speed limits on highways are too low. One p

Question

Many automotive experts believe that speed limits on highways are too low. One particular expert has stated that he thinks that most drivers drive at speeds that they consider safe. He suggested that the “correct” speed limit should be set at the 85th percentile. Suppose that a random sample of 400 speeds on a highway where the limit is 60 mph was recorded

. (a) Find the “correct” speed limit or the 85th percentile.

(b) Find all of the quartiles: 25th, 50th, and 75th percentile.

(c). If a car’s speed was 65 mph, what percentile would this be.

Excel!!

Speeds 66 71 65 72 69 83 70 62 75 71 77 65 64 66 78 69 72 77 68 72 76 65 68 66 65 71 70 73 72 76 68 67 72 76 67 71 65 69 71 67 73 78 67 71 71 65 58 67 64 72 76 78 71 70 62 70 68 72 75 76 76 68 62 75 60 66 79 76 70 71 69 73 73 76 73 68 78 72 74 60 73 88 72 67 76 70 65 76 66 74 70 63 74 62 72 68 73 78 66 74 68 72 68 73 66 75 79 70 75 63 68 78 70 72 61 71 73 74 64 76 68 79 72 67 71 65 73 75 67 73 72 60 70 63 68 73 67 75 72 68 69 66 64 68 72 69 72 64 70 67 59 73 74 67 69 69 87 62 72 71 69 65 67 67 76 73 78 70 69 73 72 67 78 71 66 63 72 67 65 71 64 70 73 71 71 68 69 63 75 67 75 69 65 69 63 63 68 70 82 68 69 72 66 70 72 71 66 71 70 72 65 72 68 81 71 65 73 71 62 73 63 72 71 67 64 63 68 78 76 76 73 79 63 68 76 75 73 66 68 66 69 62 70 79 85 72 76 71 68 63 72 70 61 70 72 72 74 66 57 72 70 64 70 65 68 68 70 70 77 57 64 74 76 69 68 78 68 75 66 67 74 75 68 73 67 67 72 69 78 67 74 85 73 76 73 72 66 69 65 75 66 76 75 79 68 78 78 73 83 67 64 71 73 71 73 58 65 79 68 73 74 59 79 71 71 76 72 62 74 68 72 67 68 67 69 74 67 82 71 74 73 68 73 71 68 65 69 70 71 68 67 75 71 65 57 66 79 66 76 63 75 72 73 65 68 75 67 61 70 69 69 70 74 71 72 69 71 75 72 72 73 75 59 70 71 77 72 74 67 72 72 67 75 72 69 68 70 70 76 58

Explanation / Answer

Given data is of speeds on a highway where the limit is 60 mph was recorded

Given that,

sample size = n = 400

A ) we want to Find the “correct” speed limit or the 85th percentile.

By using excel we can calculate the Percentile as

Put all the data in excel then

Use excel command =PERCENTILE(array,k)

=PERCENTILE(select all the data,0.85)

= 75

So, “correct” speed limit or the 85th percentile = 75

B ) we want to calculate all the Quartiles i.e. Q1,Q2,Q3

By using excel we can calculate quartiles as

Put all the data in excel worksheet then use command

=QUARTILES(array,quart)

For Q1   =QUARTILES(select all the data,1)

For Q2 =QUARTILES(select all the data,2)

For Q3 =QUARTILES(select all the data,3)

we get Q1 =25th percentile =67

Q2 = 50th percentile =70 ,

Q3 =75th percentile = 73

C ) If a car’s speed was 65 mph, then it is 15th percentile.

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