The weights of adult men in a population is normally distributed with a mean of

Question

The weights of adult men in a population is normally distributed with a mean of 150 pounds and a standard deviation of 15 pounds. If an adult man is selected at random (for a, b, and c) a. What is the probability that the person weighs less than 140 pounds? b. What is the probability that the person weighs more than 175 pounds? c. What is the probability that the person weighs between 150 pounds and 175 pounds? d. If a sample of 25 adult men are selected at random from the above population what is the probability that the mean weight of those 25 adult men is less than 148 pounds?

Explanation / Answer

Normal Distribution
Mean ( u ) =150
Standard Deviation ( sd )=15
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a.
P(X < 140) = (140-150)/15
= -10/15= -0.6667
= P ( Z <-0.6667) From Standard Normal Table
= 0.2525                  

b.
P(X > 175) = (175-150)/15
= 25/15 = 1.6667
= P ( Z >1.667) From Standard Normal Table
= 0.0478                  

c.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 150) = (150-150)/15
= 0/15 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(X < 175) = (175-150)/15
= 25/15 = 1.6667
= P ( Z <1.6667) From Standard Normal Table
= 0.95221
P(150 < X < 175) = 0.95221-0.5 = 0.4522                  

d.
P(X < 148) = (148-150)/15/ Sqrt ( 25 )
= -2/3= -0.6667
= P ( Z <-0.6667) From Standard NOrmal Table
= 0.2525

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