Question

6. The heights of women are normally distributed with a mean of 65 in. and a standard deviation of 2.5 in. The heights of men are normally distributed with a mean of 70 in. and a standard deviation of 3.0 in. Relative to their peers, who would be considered taller: A 68 in. woman or a 74 in. man?

7. The lengths of adult blue whales are normally distributed with a mean of 30 meters and a standard deviation of 6 meters. What is the probability that a randomly selected adult blue whale would have a length that differs from the population mean by less than 3 meters?

Thank you for answering!!!

Answer 1

Solution :

Given that ,

6) mean = = 65 in. ( women)

standard deviation =  = 2.5 in.

x = 68 in.

Using z-score formula,

z = x - /   

z = 68 - 65 / 2.5

z = 1.20 ( women)

mean = = 70 in. ( man)

standard deviation =  = 3.0 in.

x = 74 in.

Using z-score formula,

z = x - /   

z = 74 - 70 / 3.0

z = 1.33 ( man)

man would be considered taller

7) Given that ,

mean = = 30

standard deviation = = 6

± 3 = 27, 33

P(27 < x < 33)

= P[(27 - 30)/ 6) < (x - ) /  < (33 - 30) / 6) ]

=P( -0.5 < z < 0.5)

= P(z < 0.5) - P(z < -0.5)

Using z table,

= 0.6915 - 0.3085

= 0.3830