Suppose medical records indicate that

the length of newborn babies (in

inches) is normally distributed with a

mean of 20 and a standard deviation of

2.6. Find the probability that a given

infant is between 14.8 and 25.2 inches

long.

Step-by-step explanation:

Let x be the random variable representing the the length of newborn babies (in inches). Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ) / σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 20 inches

σ = 2.6 inches

the probability that a given infant is between 14.8 and 25.2 inches long is expressed as

P (14.8 ≤ x ≤ 25.2)

For x = 14.8,

z = (14.8 - 20) / 2.6 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.023

For x = 25.2

z = (25.2 - 20) / 2.6 = 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.98

Therefore,

P (14.8 ≤ x ≤ 25.2) = 0.98 - 0.23 = 0.75