SOLUTION: (i).The length of human pregnancies from conception to birth approximates a normal distribution with a mean of 266 days and a variance of 256 days. What proportion of all pregnanc

Question 909978: (i).The length of human pregnancies from conception to birth approximates a normal distribution with a mean of 266 days and a variance of 256 days. What proportion of all pregnancies will last between 240 days and 270 days (roughly between 8 and 9 months)? Draw a normal curve to illustrate your probability.
(ii). What length of time marks the shortest 70% of all pregnancies? Draw a normal curve to illustrate your probability.

Found 2 solutions by ewatrrr, stanbon:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
m = 266, sd = 16
I) normalcdf(240,270,266,16)
ii)z = inv Norm(.30) = (X-266)/16
16invNorm(.30) + 266 = X
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(i).The length of human pregnancies from conception to birth approximates a normal distribution with a mean of 266 days and a variance of 256 days. What proportion of all pregnancies will last between 240 days and 270 days (roughly between 8 and 9 months)? Draw a normal curve to illustrate your probability.
Draw a normal curve ; plot mean = 266 in the middle ; plot 240 to the left
adn 270 to the right of the mean.
z(240) = (240-266)/16 = -26/16 = -13/8
z(270) = (270-266)/16 = 4/16 = 1/4
P(240 < x < 270) = P(-13/8< z < 1/4) = normalcdf(-13/8,1/4) = 0.5466
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(ii). What length of time marks the shortest 70% of all pregnancies? Draw a normal curve to illustrate your probability.
Find the z-value with a left tail of 0.7
invNorm(0.7) = 0.5244
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Find the corresponding time value::
x = z*s + u
x = 0.5244*16 + 266 = 274.39 days
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Cheers,
Stan H.
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