Question

Having this information:

Arm length data

Male Mean: 75.002 Standard deviation: 3.414

Female Mean: 68.l578 Standard deviation: 3.821

answer the following questions:

1.What is the probability that a woman will have an arm length above the male mean arm length? What proportion of women that should have longer arms than the male mean?

2. Give the proportion of men that should have shorter arms than the female mean.

3.Sketch the curve and the shaded regions that illustrates the proportion of women with arm lengths within 1.5 standard deviations of the mean. Use MINITAB to calculate the probability.

Pleas help!! an explanation would be awesome! Thank you!

Answer 1

Assume normal distribution of length of arm of woman, define the standard random variable Z as

Where X denote length of arm of a women

1) Using normal table we get

So 4.65% of women that should have longer arms than the male mean

2) Assume normal distribution of length of arm of man, define the standard random variable Z as

Where Y denote length of arm of a men

1) Using normal table we get

So 3.01% of men that should have shorter arms than the female mean.

3) Using Normal table we have