Question

At St. Eligius Hospital, the weights of newborn babies follow a Normal distribution, with a mean of 7.5 pounds and a standard deviation of 1.2 pounds.

If Dr. Cavanero tells a mother that her newborn baby has a weight that is at the third quartile (or Q3), this means the baby must weigh approximately _____.

Answer 1

The baby must weigh approximately 8.31 pounds.

Explanation:

We are given the following information in the question:

Mean, μ = 7.5 pounds

Standard Deviation, σ = 1.2 pounds

We are given that the distribution of weights of newborn babies is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

We have to find the third quartile or
`Q_3`

We have to find the value of x such that the probability is 0.75

`P( X < x) = P( z < \displaystyle(x - 7.5)/(1.2))=0.75`

Calculation the value from standard normal z table, we have,

`\displaystyle(x - 7.5)/(1.2) = 0.674\\\\x = 8.3088 \approx 8.31`

Thus, the baby must weigh approximately 8.31 pounds.