students were asked to track how many snacks they ate per day during a week. the data set below shows the number of snacks each student consumed daily:
\{6, 3, 4, 7, 5, 3, 5, 4, 6, 8, 5, 7, 5, 2, 5\}. what is the probability that a student ate at least 6 snacks per day?

use the geogebra spreadsheet to find the mean and standard deviation. use these values to create a normal distribution for the data set. then use the geogebra probability calculator to solve the problem.

type your answer in the space provided. (ensure to type two decimal places only if your answer is not an exact whole number.)

about % of the students student ate at least 6 snacks, with mean snacks and standard deviation snacks.

Question

students were asked to track how many snacks they ate per day during a week. the data set below shows the number of snacks each student consumed daily:
\{6, 3, 4, 7, 5, 3, 5, 4, 6, 8, 5, 7, 5, 2, 5\}. what is the probability that a student ate at least 6 snacks per day?

use the geogebra spreadsheet to find the mean and standard deviation. use these values to create a normal distribution for the data set. then use the geogebra probability calculator to solve the problem.

type your answer in the space provided. (ensure to type two decimal places only if your answer is not an exact whole number.)

about   % of the students student ate at least 6 snacks, with mean   snacks and standard deviation   snacks.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Sample Mean", "Sample Standard Deviation", "Normal Distribution Probability" ], "new_concepts": [], "current_concepts": [ "Sample Mean", "Sample Standard Deviation", "Normal Distribution Probability" ] } ## Calculate the sample mean Using the *Sample Mean* knowledge point $$ \begin{aligned} n &= 15\ \sum x_i &= 6+3+4+7+5+3+5+4+6+8+5+7+5+2+5 = 75\ \mu &= \frac{75}{15} = 5 \end{aligned} $$ ## Calculate the sample standard deviation Using the *Sample Standard Deviation* knowledge point $$ \begin{aligned} \sum x_i^2 &= 6^2+3^2+4^2+7^2+5^2+3^2+5^2+4^2+6^2+8^2+5^2+7^2+5^2+2^2+5^2\ &= 36+9+16+49+25+9+25+16+36+64+25+49+25+4+25 = 413\ s &= \sqrt{\frac{\sum x_i^2 - n\mu^2}{n-1}} = \sqrt{\frac{413 - 15(25)}{14}} = \sqrt{\frac{38}{14}} \approx 1.6475 \end{aligned} $$ ## Calculate the normal distribution probability Using the *Normal Distribution Probability* knowledge point $$ \begin{aligned} Z &= \frac{6 - 5}{1.6475} \approx 0.6070\ P(X \ge 6) &= P(Z \ge 0.6070) \approx 0.2719\ \text{Percentage} &\approx 27.19\% \end{aligned} $$ About 27.19 % of the students ate at least 6 snacks, with mean 5 snacks and standard deviation 1.65 snacks. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Normal Distribution Probability" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the sample mean

Calculate the sample standard deviation

Calculate the normal distribution probability

Answer: