Question

3. A wire-bounding process is said to be in control if the mean pull strength is 10 pounds.
It is known that the pull-strength measurements are normally distributed with a standard
deviation of 2. 4 pounds. Periodically, a random sample of certain size are taken from
this process.
a) If the mean pull strength is indeed 10 pound, what is the probability that a randomly
selected sample results a pull strength of less than 7. 75 pounds?
b) If the mean pull strength is indeed 10 pound, what is the probability that a randomly
selected sample of 40 results a mean pull strength of less than 7. 75 pounds?
c) If the mean pull strength is indeed 10 pound, what is the probability that a randomly
selected sample of 7 results a mean pull strength of less than 7. 75 pounds?

Answer 1

Define random variable X : pull-strength measurements

X is normally distributed with Mean = and Standard deviation =

a) Here we have to find P(X < 7.75)

where z is standard normal variable.

(Round to 2 decimal)

= 0.1736 (From statistical table of z values)

Probability that a randomly selected sample results a pull strength of less than 7. 75 pounds is 0.1736

b) n = 40

As distribution of random variable X is normal, so distribution of sample mean is also normal with mean= and standard deviation =

(Round to 4 decimal)

  

= P(z < -5.93) (Round to 2 decimal)

= 0 (From statistical table of z values)

Probability that a randomly selected sample of 40 results a mean pull strength of less than 7. 75 pounds is 0

c) n = 7

As distribution of random variable X is normal, so distribution of sample mean is also normal with mean= and standard deviation =

(Round to 4 decimal)

  

= P(z < -2.48) (Round to 2 decimal)

= 0.0066    (From statistical table of z values)

Probability that a randomly selected sample of 7 results a mean pull strength of less than 7. 75 pounds is 0.0066.