Questions: QUESTION Z - 1 POINT The amount of soda consumed by Americans per day is normally distributed with a mean of 12.1 ounces and a standard deviation of 5.06 ounces. What is the probability that more than 10 ounces of soda are consumed by women over 50 ? Round all answers to 3 decimal places where possible. Provide your answer below: P(x>10)=

QUESTION Z - 1 POINT
The amount of soda consumed by Americans per day is normally distributed with a mean of 12.1 ounces and a standard deviation of 5.06 ounces.
What is the probability that more than 10 ounces of soda are consumed by women over 50 ? Round all answers to 3 decimal places where possible.

Provide your answer below:
P(x>10)=

Transcript text: QUESTION Z - 1 FOINT The amount of soda consumed by Americans per day is normally distributed with a mean of 12.1 ounces and a standard deviation of 5.06 ounces. What is the probability that more than 10 ounces of soda are consumed by women over 50 ? Round all answers to 3 decimal places where possible. Provide your answer below: \[ P(x>10)= \] $\square$

Solution

Solution Steps

Step 1: Define the Problem

We are tasked with finding the probability that more than $10$ ounces of soda are consumed by women over $50$ years old, given that the amount of soda consumed is normally distributed with a mean ($\mu$) of $12.1$ ounces and a standard deviation ($\sigma$) of $5.06$ ounces.

Step 2: Calculate the Z-Score

To find the probability $P(X > 10)$, we first calculate the Z-score for $X = 10$ using the formula:

\[ Z = \frac{X - \mu}{\sigma} \]

Substituting the values:

\[ Z = \frac{10 - 12.1}{5.06} \approx -0.415 \]

Step 3: Find the Probability

Next, we find the cumulative probability $P(X \leq 10)$ using the Z-score. This is represented as:

\[ P(X \leq 10) = \Phi(Z_{start}) = \Phi(-0.415) \]

From the calculations, we find:

\[ P(X \leq 10) \approx 0.661 \]

Step 4: Calculate the Probability of Interest

To find the probability of consuming more than $10$ ounces, we use the complement: