Question

the number of fruit snacks in each package is assumed to have 13 pieces per package, on average. calian opened up 34 packs of fruit snacks and found the average number of snacks to be 12.1 with a standard deviation of 1.02.

\\(df =\\)

round answers to three decimal places.

\\(se =\\)

\\(t =\\)

what is the probability of finding a sample of size 34 with an average of 12.1 fruit snacks or less?

enter answer as a decimal to 4 decimal places

use the \\(t\\)-distribution tool to answer the question and enter the \\(t\\) score for \\(x\\).

Explanation:

Calculate degrees of freedom

Using the t-Distribution knowledge point

$$ df = n - 1 = 34 - 1 = 33 $$

Calculate standard error

Using the Standard Error knowledge point

$$ SE = \frac{s}{\sqrt{n}} = \frac{1.02}{\sqrt{34}} \approx 0.174925 \approx 0.175 $$

Calculate t-score

Using the One-Sample t-Test knowledge point

$$ t = \frac{\bar{x} - \mu}{SE} = \frac{12.1 - 13}{\frac{1.02}{\sqrt{34}}} \approx \frac{-0.9}{0.174925} \approx -5.14506 \approx -5.145 $$

Calculate probability

Using the t-Distribution knowledge point

$$ P(T_{33} \le -5.145) \approx 0.0000056 \approx 0.0000 $$

Answer:

Question 1

\(df =\) <blank>33</blank>

Question 2

\(SE =\) <blank>0.175</blank>

Question 3

\(t =\) <blank>-5.145</blank>

Question 4

What is the probability of finding a sample of size 34 with an average of 12.1 fruit snacks or less?
<blank>0.0000</blank>