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What percent of the children spend over 10 hours per day unsupervised? (Round your answer to four decimal places.) DPart je s0% of the chidren spend at lest how tong per day unsupervised? (Round your answer to two decimal places) hours

What percent of the children spend over 10 hours per day unsupervised? (Round your answer to four decimal places.) DPart je s0% of the chidren spend at lest how tong per day unsupervised? (Round your answer to two decimal places) hours

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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I've been stuck on solving these two problems so any help is appreciated! step by step explanation would be great.

Suppose 4-year-olds in a certain country average 3 hours a day unsupervised and that most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.8 hours and the amount of time spent alone is normally distributed. We randomly survey one 4-year-old living in a rural area. We are interested in the amount of time the child spends alone per day. **Part (a):** Find the probability that the child spends less than 1 hour per day unsupervised. Write the probability statement: \[ P(X < 1) \] What is the probability? (Round your answer to four decimal places.) \[ 0.1335 \] **Sketch the graph:** The graph displays a normal distribution curve with the shaded area representing the probability of a child spending less than 1 hour unsupervised. The curve is centered around the mean (3 hours) with a standard deviation of 1.8 hours. The shaded area is located to the left of 1 on the horizontal axis, indicating the probability of spending less than 1 hour. Two graphs are presented underneath for potential selection but are not distinguished in the explanation. **Part (b):** What percent of the children spend over 10 hours per day unsupervised? (Round your answer to four decimal places.) \[ \] (No answer provided in the image) **Part (c):** 90% of the children spend at least how long per day unsupervised? (Round your answer to two decimal places.) \[ \] hours (No answer provided in the image) **Notes:** The page is designed to guide students through calculating probabilities using a normal distribution with real-world context. It incorporates statistical interpretation, probability calculation, and visual representation.
Transcribed Image Text:Suppose 4-year-olds in a certain country average 3 hours a day unsupervised and that most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.8 hours and the amount of time spent alone is normally distributed. We randomly survey one 4-year-old living in a rural area. We are interested in the amount of time the child spends alone per day. **Part (a):** Find the probability that the child spends less than 1 hour per day unsupervised. Write the probability statement: \[ P(X < 1) \] What is the probability? (Round your answer to four decimal places.) \[ 0.1335 \] **Sketch the graph:** The graph displays a normal distribution curve with the shaded area representing the probability of a child spending less than 1 hour unsupervised. The curve is centered around the mean (3 hours) with a standard deviation of 1.8 hours. The shaded area is located to the left of 1 on the horizontal axis, indicating the probability of spending less than 1 hour. Two graphs are presented underneath for potential selection but are not distinguished in the explanation. **Part (b):** What percent of the children spend over 10 hours per day unsupervised? (Round your answer to four decimal places.) \[ \] (No answer provided in the image) **Part (c):** 90% of the children spend at least how long per day unsupervised? (Round your answer to two decimal places.) \[ \] hours (No answer provided in the image) **Notes:** The page is designed to guide students through calculating probabilities using a normal distribution with real-world context. It incorporates statistical interpretation, probability calculation, and visual representation.
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