Question

No, because it is smaller than the minimum "usual" value (10) Heights of men on a baseball team have a bell-shaped distribution with a mean of 185 cm and a standard deviation of 5 cm. Using the empirical rule, what is the approximate percentage of the men between the following values? Please show your work! A. 4. % of the men are between 180 cm and 190 cm. B. % of the men are between 170 cm and 200 cm.

Answer 1

Let X:Heights of men on basket ball team

Let X: Heights of men on basket ball team Z = X - mu/sigma To find P(180 < X < 190) = P(180 - 185/5 < Z < 190 - 185/5) = P(-1 < Z < 1) By using impirical rule, 68% of data falls within the first standard deviation from the mean. Therefore, P(180 < X < 190) = 0.68 To find P(170 < X < 200) = P(170 - 185/5 < Z < 200 - 185/5) = P(-3 < Z < 3) By using impirical rule, 99.7% of data falls within three standard deviation from the mean. Therefore, P(170 < X < 200) = 0.997

A)To find

$P(180<X<190)=P(\frac{180-185}{5}<Z<\frac{190-185}{5})=P(-1<Z<1)$

By using impirical rule, 68% of data falls within the first standard deviation from the mean.

Therefore,

$P(180<X<190)=0.68$

B)To find

By using impirical rule, 99.7% of data falls within three standard deviation from the mean.

Therefore,