Question

Janssen et al. studied Americans ages 60 and over. They estimated the mean body mass index of women over age 60 with normal skeletal muscle to be 23.1 with a standard deviation of 3.7. Using these values as the population mean and standard deviation for women over age 60 with normal skeletal muscle index, find the probability that 45 randomly selected women in this age range with normal skeletal muscle index will have a mean BMI (a) greater than 24. (b) less than 22.5 mg. (c) Between 22.6 and 23 mg.

Answer 1

Solution :

Given that ,

= 23.1

= / n = 3.7/ 45 = 0.552

a) P( > 24) = 1 - P( < 24 )

= 1 - P[( - ) / < (24 - 23.1) / 0.552]

= 1 - P(z <1.63 )   

= 1 - 0.9484

= 0.0516

b) P( < 22.5) = P(( - ) / < (22.5 - 23.1) / 0.552)

= P(z < -1.09)

Using z table

= 0.1379

c) P(22.6 < < 23)  

= P[(22.6 - 23.1) / 0.552 < ( - ) / < (23 - 23.1) / 0.552 )]

= P(-0.91 < Z < -0.18)

= P(Z < -0.18) - P(Z < -0.91)

Using z table,  

= 0.4286 - 0.1814  

= 0.2472