Question

Variance: A company produces several thousand nominally identical resistors each day. An operator tested a sample of 100 resistors and obtained an average resistance of Ro=100 ohms with a standard deviation of S= 10 ohms.

(a) If the operator discards 5% of the resistors as too high and another 5% as too low find the high and low acceptable limits?

(b) What is the level of significance, level of confidence and the confidence interval for resistors having a value greater than 116.5?

(c) If a resistor is selected at random what is the probability that the resistance is between 105 Ohms and 110 Ohms?

(d) At the end of the day, another test is performed on another batch of resistors. What is the probability that the mean value of this second test will be within 1 ohm of the mean obtained in the first sample of 100 resistors described in part (a)? Will this depend on the size of the second sample tested?

Answer 1

a)

z= 1.645 for top 5 % and -1.645 for bottom 5%

X = mean + z*sd

high limit = 100 + 1.645 * 10 = 116.45

low limit = 100 -1.645*10 = 83.55

b)

P(X > 116.5)

= P(Z >(116.5 - 100)/10)

= P(Z > 1.65)

= 0.0495

c)

P(105 < X < 110)

= P( 0.5 < Z < 1)

= 0.1499