1. Newborn males have a mean length of 49.9cm with a standard deviation of 1.9cm

Question

1. Newborn males have a mean length of 49.9cm with a standard deviation of 1.9cm. For the purpose of this problem, assume that their lengths fit a normal distribution. (a) Identify and ? (b) Find the z-score of a newborn male of length 52em. S 11 1.los 24315Y 1.9 (e) Translate the statement "the probability a newborn male is of length less than 52cm" into a probability statement with the z-score (use symbols!). (d) Find the probability that a newborn male is shorter than 52em. (e) Find the probability that a newborn male is shorter than 47cm. (f) Find the probability that a newborn male is taller than 47cm. (g) Find the probability that a newborn male is taller than 53cm.

Explanation / Answer

c)
P(x <52) we get the z value = 1.1053
we need to find P(z < 1.1053 ) = 0.8655

d) mean = 49.9 , s = 1.9

P(x < 52)

z = ( x - mean) / s
= ( 52 - 49.9)/1.9
= 1.1053
P(x < 52) = P(z < 1.1053) = 0.8655 by using standard normal table

e)
P(x < 47)

z = ( x - mean) / s
= ( 47 - 49.9)/1.9
= -1.5263

P(x < 47) = P(z < -1.5263) = 0.0635 by using standard normal table

f)
P(x > 47)

z = ( x - mean) / s
= ( 47 - 49.9)/1.9
= -1.5263

P(x > 47) = P(z > -1.5263) = 0.9365 by using standard normal table

g)
P(x > 53)

z = ( x - mean) / s
= ( 53 - 49.9)/1.9
= 1.6316

P(x > 53) = P(z >1.6316) = 0.0514 by using standard normal table

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