Questions: "How many licks to the center of a Tootsie pop?" In an attempt to answer this question, a university asked 95 volunteers to count the number of licks required before reaching the chocolate center. The mean number of licks was 316.5 and the standard deviation was 157.2.

"How many licks to the center of a Tootsie pop?" In an attempt to answer this question, a university asked 95 volunteers to count the number of licks required before reaching the chocolate center. The mean number of licks was 316.5 and the standard deviation was 157.2.

Transcript text: "How many licks to the center of a Tootsie pop?" In an attempt to answer this question, a university asked 95 volunteers to count the number of licks required before reaching the chocolate center. The mean number of licks was 316.5 and the standard deviation was 157.2.

Solution

Solution Steps

Step 1: Calculate the Confidence Interval

To determine the 90% confidence interval for the mean number of licks to reach the center of a Tootsie pop, we use the formula for the confidence interval of a population mean with unknown variance and a large sample size:

\[ \bar{x} \pm z \frac{s}{\sqrt{n}} \]

Where:

\(\bar{x} = 316.5\) (sample mean)
\(s = 157.2\) (sample standard deviation)
\(n = 95\) (sample size)
\(z\) is the z-score corresponding to the 90% confidence level, which is approximately \(1.64\).

Substituting the values into the formula:

\[ 316.5 \pm 1.64 \cdot \frac{157.2}{\sqrt{95}} \]

Calculating the margin of error:

\[ \frac{157.2}{\sqrt{95}} \approx 16.086 \]

Thus, the margin of error is:

\[ 1.64 \cdot 16.086 \approx 26.38 \]

Now, we can calculate the confidence interval:

\[ (316.5 - 26.38, 316.5 + 26.38) = (290.12, 342.88) \]

Step 2: Interpret the Confidence Interval

The calculated 90% confidence interval is:

\[ (289.97, 343.03) \]

This means that we are 90% confident that the true mean number of licks to reach the center of a Tootsie pop lies within this interval.