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The heights of kindergarten children are approximately normally distributed with the following. (Give your answers correct to four decimal places.)
μ = 45 and σ = 3.2 inches
(a) If an individual kindergarten child is selected at random, what is the probability that he or she has a height between 42.7 and 47.3 inches?
(b) A classroom of 25 of these children is used as a sample. What is the probability that the class mean x is between 42.7 and 47.3 inches?
(c) If an individual kindergarten child is selected at random, what is the probability that he or she is taller than 47.2 inches?
(d) A classroom of 25 of these kindergarten children is used as a sample. What is the probability that the class mean x is greater than 47.2 inches? Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website! μ = 45 and σ = 3.2 inches
(a) If an individual kindergarten child is selected at random, what is the probability that he or she has a height between 42.7 and 47.3 inches?
P(42.7< x < 47.3) = P( -2.3/3.2 < z < 2.3/3.2) = normalcdf(-.7188, .7188)
............
P(42.7< xbar < 47.3) = P(-2.3/.64 < z < 2.3/.64) = normalcdf( -3.5938, 3.5938)
.......
P( x > 47.2) = P(z > 2.2/3.2) = normaldcdf( .6875, 100)
.......
P( xbar > 47.2) = P(z > 2.2/.64) = normalcdf(3.4375, 100)
