Statistics: (my book says the answer for 31.a is 51, and b is 17, but I got some

Question

Statistics:

(my book says the answer for 31.a is 51, and b is 17, but I got something different.)

29. The mean speed of a sample of vehicles along a stretch of highway is 67 miles per hour, with a standard deviation of 4 miles per hour. Estimate the percent vehicles whose speeds are between 63 miles per hour and 71 miles per hour. (Assume the data set has a bell-shaped distribution.) 31. Use the sample statistics from Exercise 29 and assume the number of vehicles in the sample is 75. (a) Estimate the number of vehicles whose speeds are between 63 miles per hour and 71 per hour (b) In a sample of 25 additional vehicles, about how many vehicles would you expect to have speeds between 63 miles per hour and 71 miles per hour?

Explanation / Answer

1) Mean = 67miles / hours;

st. Dev=4;

From Normal distribution graph P(x<=63)

(63-67)/4 = -1;

we have P(x<=63) = 0.15866 or 15.866%;

P(x<=71)

(71-67)/4=1;

P(x<=71) = 0.84134 = 84.134%;

The vehicles between 63 and 71 are 68.268%;

Now the sample space is 75 vehicles;

so number of vehicles between 63 and 71 are 75*0.68268=51;

Number of vehicles between 63 and 71 when there are 25 additional vehicles is 25*0.68268=17 additional vehicles;

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