Question

When Mayerlin goes bowling, her scores are normally distributed with a mean of 175 and a standard deviation of 13. Using the empirical rule, what percentage of the games that Mayerlin bowls does she score between 162 and 188?

Answer 1

Answer:

68%

Step-by-step explanation:

The Empirical rule formula is given as:

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

Where

μ is the population mean

σ is the population standard deviation.

Step 1

Find the number of standard deviations from the mean

μ - xσ and μ + xσ

μ = 175

σ = 13

For 162

175 - 13x = 162

175 - 162 = 13x

13 = 13x

x = 13/13

x = 1

For 188

175 + 13x = 188

13x = 188 - 175

13x = 13

x = 13/13

x = 1

Hence, the data falls with 1 standard deviation of the mean

Therefore, percentage of the games that Mayerlin bowls does she score between 162 and 188 is 68%