Question 24

Explanation

Variables and Parameters

Let $X$ be the weight of a newborn baby (normally distributed)

• Mean $\mu = 3{,}200$ grams
• Standard deviation $\sigma = 450$ grams

Standardization (Z-score)

We need to convert weight limits to Z-scores to use the standard normal distribution table.

Lower Bound

For $x_1 = 2{,}750$ grams

Upper Bound

For $x_2 = 3{,}650$ grams

Calculating Probability

We want to find $P(2{,}750 \leq X \leq 3{,}650)$, which is equivalent to $P(-1 \leq Z \leq 1)$ in the standard normal distribution.

Using the cumulative distribution function (CDF) of the normal distribution

In the notation of the standard normal distribution CDF, $P(Z \leq z)$ is often written as $\Phi(z)$ or $P(Z < z)$ (since the normal distribution is continuous, $P(Z \leq z) = P(Z < z)$).

Therefore, $P(-1 \leq Z \leq 1) = P(Z \leq 1) - P(Z < -1)$

The most appropriate answer is A.