Current learning objective: Calculations of Probabilities
Question 25
Score: 0 of 4 points
The amount of hot chocolate dispensed by a hot chocolate machine into a cup follows a normal distribution
with a mean of 12.1 ounces and a standard deviation of 4 ounces.
Find the probability that the cup contains more than 8 ounces of hot chocolate.
(Round -score to 2 decimal places in your calculation if needed)
A 0.849
B 0.891
C 0.797
D 0.736

Question

Current learning objective: Calculations of Probabilities
Question 25
Score: 0 of 4 points
The amount of hot chocolate dispensed by a hot chocolate machine into a cup follows a normal distribution
with a mean of 12.1 ounces and a standard deviation of 4 ounces.
Find the probability that the cup contains more than 8 ounces of hot chocolate.
(Round

-score to 2 decimal places in your calculation if needed)
A 0.849
B 0.891
C 0.797
D 0.736

UpStudy AI · Accepted Answer

1. The amount of hot chocolate dispensed, $$ X $$, is normally distributed with mean $$\mu = 12.1$$ ounces and standard deviation $$\sigma = 4$$ ounces.

2. We wish to find the probability that a cup contains more than 8 ounces, that is, $$ P(X > 8) $$.

3. Standardize the variable $$ X $$ to convert it into a standard normal variable $$ Z $$ using:
   $$
   Z = \frac{X - \mu}{\sigma}
   $$
   For $$ X = 8 $$:
   $$
   z = \frac{8 - 12.1}{4} = \frac{-4.1}{4} = -1.025
   $$
   Rounding to two decimal places, $$ z \approx -1.03 $$.

4. The probability we need becomes:
   $$
   P(X > 8) = P(Z > -1.03)
   $$

5. Using the symmetry of the normal distribution:
   $$
   P(Z > -1.03) = P(Z < 1.03)
   $$

6. Looking up the cumulative probability for $$ z = 1.03 $$ in the Z-table, we find:
   $$
   \Phi(1.03) \approx 0.849
   $$

7. Therefore, the probability that the cup contains more than 8 ounces of hot chocolate is approximately $$ 0.849 $$.

The correct answer is A $$ 0.849 $$.
The probability that the cup contains more than 8 ounces of hot chocolate is approximately 0.849.

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