Question

1. Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard deviation of 15. Find the probability that x assumes a value:

1. less than 48

2. greater than 87

           

3. between 56 and 70

Answer 1

This is a normal distribution question with



a) P(x < 48.0)=?
The z-score at x = 48.0 is,

z = -1.1333
This implies that



b) P(x > 87.0)=?
The z-score at x = 87.0 is,

z = 1.4667
This implies that
P(x > 87.0) = P(z > 1.4667) = 1 - 0.92877115855788




c) P(56.0 < x < 70.0)=?

This implies that
P(56.0 < x < 70.0) = P(-0.6 < z < 0.3333) = P(Z < 0.3333) - P(Z < -0.6)
P(56.0 < x < 70.0) = 0.6305460803074295 - 0.2742531177500736

PS: you have to refer z score table to find the final probabilities.
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