Question

In: Statistics and Probability

The lengths of one-year-old baby girls, in a certain country, can be described using a Normal...

The lengths of one-year-old baby girls, in a certain country, can be described using a Normal distribution with a mean of 29 inches and a standard deviation of 1.2 inches. Use this information to answer the below.

a. What is the probability a randomly chosen one-year girl, from this population, is between 27 and 31 inches tall?

b. How tall is a one-year old girl, from this population, who is in the 85th percentile?

c. What is the z-score (standardized score) for a 28 inch tall girl? .

d. Suppose a random sample of 20 one-year old girls is taken from this population. What is the probability that the average height is less than 29 inches?

Solutions

Expert Solution

Solution :

Given that ,

mean = = 29

standard deviation = = 1.2

a. P(27 < x < 31) = P((27 - 29)/ 1.2) < (x - ) / < (31 - 29) / 1.2) )

= P(-1.67 < z < 1.67)

= P(z < 1.67) - P(z < -1.67)

= 0.9525 - 0.0475

= 0.905

Probability = 0.905

b. Using standard normal table,

P(Z < z) = 85%

P(Z < 1.04) = 0.85

z = 1.04

Using z-score formula,

x = z * +

x = 1.04 * 1.2 + 29

x = 30.25

85th percentile =30.25

c. x = 28

z = x -   /

= 28 - 29 / 1.2 = -0.83

z-score = -0.83

d. n = 20

= 29 and

= / n = 1.2 / 20 = 0.2683

P( < 29) = P(( - ) / < (29 - 29) / 0.2683)

= P(z < 0)

Using standard normal table,

= 0.5

Probability = 0.5


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