On the planet of Mercury, 4-year-olds average 2.8 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.3 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to 4 decimal places where possible.
On the planet of Mercury, 4-year-olds average 2.8 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.3 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to 4 decimal places where possible.
![On the planet of Mercury, 4-year-olds average 2.8 hours a day unsupervised. Most of the unsupervised
children live in rural areas, considered safe. Suppose that the standard deviation is 1.3 hours and the
amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in
a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose
Mercury News) Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X - N(
b. Find the probability that the child spends less than 3.1 hours per day unsupervised.
c. What percent of the children spend over 3 hours per day unsupervised.
% (Round to 2 decimal
places)
d. 88% of all children spend at least how many hours per day unsupervised?
hours.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ba0bb6e-e2c2-4193-9e84-578f833b18f1%2Fad06d345-2f21-4318-aa2e-199d0c8fa6ac%2Fsewpj0h_processed.png&w=3840&q=75)
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Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any specific subpart to be answered then please submit that subpart only or specify the subpart in your message.
Given:
a) The distribution of X is X~N.
Answer:
Thus, the distribution of X is X~N.
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