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For women aged 18–24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. If 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140.

Respuesta :

CastleRook
the probability that their mean systolic blood pressure is greater than 140 is given by:
P(x>140)=1-P(x<X)=1-P(z<Z)
The z-score is given by:
z=(x-mu)/sig
x=140, mu=114.8, sig=13.1
plugging the values we get:
z=(140-114.8)/13.1
z=1.924

thus
P(z<1.924)=0.9719
hence:
P(x>140)=1-0.9719=0.0281

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