Question

height of men on a baseball team have a bell-shaped distribution with a mean of 171 cm and a standard deviation of 7cm and a standard deviation of 7 cm. Using the empirical rule, what is the approximate percentage of the men between the following values.
what percent of men are between 157 cm and 185 cm.
what percent of men are between 164 cm and 178 cm

Answer 1

Height of men on a baseball team have a bell-shaped distributionwith a mean of 171 cm and a standard deviation of 7 cm. Using the empirical
rule, what is the approximate percentage of the men between the following
values.
Empirical rule:If a data distributionis approximately normal then about 68 percent of the data values are within one
standard deviation of the mean (mathematically, μ ± σ, where μ is the
arithmetic mean), about 95 percent are within two standard deviations (μ ± 2σ),
and about 99.7 percent lie within three standard deviations (μ ± 3σ). This is
known as the 68-95-99.7 rule, or the empirical rule.
1. What percent of men is between 157 cm and 185 cm.157 cm = 171 cm - 14 cm = (171 - 2*σ) cm
σ = 7 cm - standard deviation
185 = 171 cm + 14 cm = (171+2*σ) cm
So, we have symmetric interval (μ ± 2σ), usingthe empirical rule probability equals:
P = 95 percent
Answer: percentageof the men between the following values is about 95 percent

2. What percent of men is between 164 cm and 178 cm
164 cm = 171 cm - 7 cm = (171 - σ) cm
σ = 7 cm - standard deviation
178 = 171 cm + 7 cm = (171 + σ) cm
So, we have symmetric interval (μ ± σ), usingthe empirical rule probability equals:
P =68 percent
Answer: percentageof the men between the following values is about 68 percent