Question

A doctor is using a growth chart for baby girls that indicates a 12-month-old baby girl has a mean weight of 20.9 pounds with a standard deviation of about 2.3 pounds. Assume that the weights are approximately normally distributed.

a) What is the probability that a randomly chosen 12-month-old baby girl weighs less than 19.05 pounds?

b) What is the probability that a randomly chosen 12-month-old baby girl weighs more than 23.5 pounds?

c) What proportion of 12-month-old baby girls weigh between 19.95 and 22.39 pounds?

Answer 1

Solution :

Given that ,

mean = = 20.9

standard deviation = = 2.3

a)

P(x < 19.05) = P[(x - ) / < (19.05 - 20.9) / 2.3]

= P(z < -0.80)

= 0.2119

Probability = 0.2119

b)

P(x > 23.5) = 1 - P(x < 23.5)

= 1 - P[(x - ) / < (23.5 - 20.9) / 2.3)

= 1 - P(z < 1.13)

= 1 - 0.8708

= 0.1292

Probability = 0.1292

c)

P(19.95 < x < 22.39) = P[(19.95 - 20.9)/ 2.3) < (x - ) /  < (22.39 - 20.9) / 2.3) ]

= P(-0.41 < z < 0.65)

= P(z < 0.65) - P(z < -0.41)

= 0.7422 - 0.3409

= 0.4013

Proportion = 0.4013