Question
)) A health psychologist was researching the role of choice in food consumption. In one experiment, the psychologist offered a group of children a choice of either a chocolate chip cookie or fresh fruit. Earlier results indicate that \( 74 \% \) of children choose the chocolate chip cookie. 4) If the earlier results are accurate, and the psychologist randomly picks 2 children to interview after the experiment, what is the mean of the number of children who chose chocolate chip cookies over fresh fruit? Write your answer as a decimal.
Ask by Weston Mills. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The mean number of children who chose chocolate chip cookies is 1.48.
Solution
The mean (expected value) of the number of children who choose chocolate chip cookies can be calculated using the formula for the expectation of a binomial distribution:
\[
\text{Mean} = n \times p
\]
Where:
- \( n = 2 \) (the number of children selected)
- \( p = 0.74 \) (the probability a child chooses a chocolate chip cookie)
Plugging in the values:
\[
\text{Mean} = 2 \times 0.74 = 1.48
\]
**Answer:**
1.48
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Simplify this solution Mind Expander
To find the mean number of children who chose chocolate chip cookies, we can utilize the expected value formula for a binomial distribution. With \( n \) being the total number of children and \( p \) being the probability of a child choosing a cookie, we have: 1. \( n = 2 \) (the two children selected) 2. \( p = 0.74 \) (the probability of choosing a cookie) The mean \( \mu \) can be calculated using the formula: \[ \mu = n \cdot p = 2 \cdot 0.74 = 1.48 \] So, the mean number of children who chose chocolate chip cookies is 1.48.
