Question

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.3 inches, and standard deviation of 3.7 inches.What is the probability that the height of a randomly chosen child is between 47.95 and 49.05 inches?Use the Normal table and give answer to 4 decimal places

Answer 1

The formula for the z-score z of a value x from a normally distributed data is given by:

`z=(x-\mu)/(\sigma)`

In this case,

`\mu=56.3,\sigma=3.7`

Therefore, the z-score of 47.95 is given by:

`z=(47.95-56.3)/(3.7)\approx-2.26`

Similarly the z-score of 49.05 is -1.96

The required probability is given by:

`Pr(-2.257\lt x\lt-1.959)`

The required probability:

`Pr(-2.26\lt x\lt-1.96)=Pr(x\lt-1.96)-Pr(x\lt-2.26)`

Hence,

`Pr(-2.26\lt x\lt-1.96)=0.025-0.0119=0.0131`