Question

Suppose the average golfer drives the ball around 214.33 yards with a standard deviation of 6.73. However, when given a new type of driver, every observation in the dataset is multiplied by 1.26. What is the new standard deviation?

a. 204.27
b. 10.81
c. 255.79
d. 9.84
e. 8.58

Answer 1

Therefore, a new standard deviation is 8.58.

Explanation:

We know that the average golfer drives the ball around 214.33 yards with a standard deviation of 6.73.

We calculate the percentage deviation, and we get

214.33 : 100%=6.73 : x%

214.33x=100·6.73

214.33x=673

x=673/214.33

x=3.1400177%

We calcualte a new type. We get that now golfer drives the ball

214.33· 1.26=270.0558

Now, we calculate a new standard deviation:

270.05558 : 100%=x : 3.1400177%

100x=270.05558 · 3.1400177

100x= 847.99

x=847.99/100

x=8.48 ≈ 8.58

Therefore, a new standard deviation is 8.58.