# Answer to Question #26443 in Statistics and Probability for ronda

Question #26443

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

what percent of men are between 157 cm and 185 cm.

what percent of men are between 164 cm and 178 cm

Expert's answer

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

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

Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

Assignment Expert28.01.16, 15:37Dear visitor,

please use panel for submitting new questions

ladona27.01.16, 07:28Heights of men on a baseball team have a bell-shaped distribution with a mean of 178 cm178 cm and a standard deviation of 5 cm5 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?

a. 168168 cm and 188188 cm

b. 163163 cm and 193193 cm

## Leave a comment