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

Answer:

The baby must weigh approximately 8.31 pounds.      

Step-by-step 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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

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

$P( X < x) = P( z < \displaystyle\frac{x - 7.5}{1.2})=0.75$  

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

$\displaystyle\frac{x - 7.5}{1.2} = 0.674\\\\x = 8.3088 \approx 8.31$

Thus, the baby must weigh approximately 8.31 pounds.