Problem 7 Four-year-olds in China average 4.5 unsupervised hours per day. Most o
ID: 3350913 • Letter: P
Question
Problem 7 Four-year-olds in China average 4.5 unsupervised hours per day. Most of the unsupervised children live in rural areas, considered safe. Suppose that the amount of unsupervised time is normally distributed with standard deviation 0.5. A Chinese 4-year-old is randomly selected from a rural area. We are interested in the amount of time the child spends alone per day In each appropriate box you are to enter either a rational number in "p/q format or a decimal value accurate to the nearest 0.01 a. (3%) In words, the random variable X inwhich weare interested is defined by X=Leck one) b. (3%) Find the probability that the child spends less than one hour per day unsupervised. P(X 10)- d.(3%) The 70th percentile of the distribution of unsupervised time is given by PXExplanation / Answer
a) X = Time that child spends alone per day
b) P(X < 1)
= P(z < (1 - 4.5)/0.5)
= P(z < -7)
= 0.00
c) P(X > 10)
= P(z > (10 - 4.5)/0.5)
= P(z > 11)
= 0.00
d) For 70th percentile, z = 0.52
Hence,
X = 4.5 + 0.52*0.5 = 4.76
i.e.
P(X < 4.76) = 0.70