Question

Please find the percentage for all the questions below.

Scores for professional golfers on 18-hole courses are bell-shaped with a mean of 72 strokes and a standard deviation of 5 strokes. Using the Empirical Rule, what is the approximate percentage of golfer scores between 62 and 82 strokes?

Percentage is:

A child's piano practice times are normally distributed with a mean of 22 minutes and a standard deviation of 6 minutes. Using the Empirical Rule, what is the approximate percentage of practice times running between 16 and 28 minutes?

Percentage is:

Weights of Old English Sheepdogs are normally distributed with a mean of 59 pounds and a standard deviation of 6 pounds. Using the Empirical Rule, what is the approximate percentage of sheepdogs weighing between 41 and 77 pounds?

Percentage is:

Answer 1

Solution:-

1) The approximate percentage of golfer scores between 62 and 82 strokes is 95%.

Mean = 72, S.D = 5

x₁ = 62

x₂ = 82

By applying normal distribution:-

z₁ = -2.0

z₂ = 2.0

According to the empirical rule, the percentage of golfer scores between 2 standard deviations is 95%.

2) The approximate percentage of practice times running between 16 and 28 minutes is 68%.

Mean = 22, S.D = 6

x₁ = 16

x₂ = 28

By applying normal distribution:-

z₁ = -1.0

z₂ = 1.0

According to the empirical rule, the percentage of practice times running between 1 standard deviations is 68%.

3) The approximate percentage of sheepdogs weighing between 41 and 77 pounds is 99.7%.

Mean = 59, S.D = 6

x₁ = 41

x₂ = 77

By applying normal distribution:-

z₁ = -3.0

z₂ = 3.0

According to the empirical rule, the percentage of sheepdogs weighing between 3 standard deviation is 99.7%.