QuestionJuly 15, 2025

The weights of newborn babies are distributed normally.with a mean of approximately 95oz and a standard deviation of 5 oz. If a newborn baby is selected at random, what is the probability that the baby weighs more than 90 oz? The probability is square (Type an integer or a decimal.)

The weights of newborn babies are distributed normally.with a mean of approximately 95oz and a standard deviation of 5 oz. If a newborn baby is selected at random, what is the probability that the baby weighs more than 90 oz? The probability is square (Type an integer or a decimal.)
The weights of newborn babies are distributed normally.with a mean of approximately 95oz and a standard deviation of 5 oz. If a newborn baby is selected at random, what is the probability that the
baby weighs more than 90 oz?
The probability is square  (Type an integer or a decimal.)

Solution
4.3(235 votes)

Answer

0.8413 Explanation 1. Calculate the Z-score Use the formula Z = \frac{X - \mu}{\sigma} where X = 90, \mu = 95, and \sigma = 5. So, Z = \frac{90 - 95}{5} = -1. 2. Find the probability using Z-table Look up the Z-score of -1 in the standard normal distribution table to find the probability that a baby weighs less than 90 oz. This value is approximately 0.1587. 3. Calculate the probability for more than 90 oz Subtract the probability found from 1: 1 - 0.1587 = 0.8413.

Explanation

1. Calculate the Z-score<br /> Use the formula $Z = \frac{X - \mu}{\sigma}$ where $X = 90$, $\mu = 95$, and $\sigma = 5$. So, $Z = \frac{90 - 95}{5} = -1$.<br />2. Find the probability using Z-table<br /> Look up the Z-score of -1 in the standard normal distribution table to find the probability that a baby weighs less than 90 oz. This value is approximately 0.1587.<br />3. Calculate the probability for more than 90 oz<br /> Subtract the probability found from 1: $1 - 0.1587 = 0.8413$.
Click to rate: