Question

n the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.1 inches, and standard deviation of 5.8 inches. A) What is the probability that a randomly chosen child has a height of less than 46.3 inches

Answer 1

The probability is 0.0643 to 4 decimal places

Explanation:

To calculate this probability, we find the z-score

Mathematically;

z-score = (x-mean)/SD

where in the question;

x = 46.3

mean = 55.1

SD = 5.8

Plugging these values, we have;

z-score = (46.3-55.1)/5.8 = -8.8/5.8 = -1.52

The probability we want to calculate is;

P(z < -1.52)

We can get this answer by using the standard normal distribution table;

Thus from the table, we have;

P(z < -1.52) = 0.064255 which is 0.0643 to 4 decimal places