The time for a human pregnancy is distributed N(39, 1.622) weeks in the US. a) A

Question

The time for a human pregnancy is distributed N(39, 1.622) weeks in the US. a) A preterm baby is defined as a baby born earlier than 37 weeks. What percentage of babies are preterm? Use 4 decimals. b) A postmature baby is born after more than 41 weeks. What percentage of babies are postmature? Use 4 decimals. c) What percentage are neither preterm nor postmature? Use 4 decimals. d) My wife says those women who have the longest 1% of pregnancies must be pretty miserable. How long do their pregnancies last? Use 2 decimals. weeks. e) My first son was born early. In fact only 37% of babies are born earlier than he was. How many weeks was it before he was born Use 2 decimals weeks.

Explanation / Answer

a)

b)

c)

d) for largest 1% ; z =2.33

hence length of pregnancy =mean +z*std deviation =39+2.33*1.62 =42.77

e) for 37% smallest ; z =-0.33

hence length of pregnancy =mean +z*std deviation = 38.47 (try 38.46 if his does not work due to rounding)

for normal distribution z score =(X-)/ here mean=       = 39.000 std deviation   == 1.62

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