Answer to High School question. Here is a photo

High School

Answered question

2022-04-22

Answer & Explanation

nick1337

Expert2023-04-29Added 777 answers

We are given that the birth weights of infants in a certain population follow a normal distribution with mean

μ = 7.75

pounds and standard deviation

σ = 1.25

pounds.
We want to determine the probability that an infant's birth weight is less than

6.625

pounds. Let X be the random variable representing the birth weights of infants.
We can standardize the normal distribution to have mean 0 and standard deviation 1 using the standard normal distribution formula:

Z = \frac{X - μ}{σ}

Substituting the given values, we get:

Z = \frac{6.625 - 7.75}{1.25} = - 0.92

The probability of an infant's birth weight being less than 6.625 pounds can be found by calculating the area under the standard normal distribution curve to the left of

Z = - 0.92

. This can be done using a standard normal distribution table or a calculator.
Using a standard normal distribution table, we can look up the probability corresponding to

Z = - 0.92

as 0.1788.
Therefore, the probability that an infant's birth weight is less than 6.625 pounds is:

P (X < 6.625) = P (Z < - 0.92) = 0.1788

This completes the solution.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High School

Didn't find what you were looking for?

Store	Original Price of Aquarium ($)
Pets Plus	118
Pet Planet	110