Question

historical data shows that the diameter of current piston rings is a normally distributed random variable with a mean of 11cm and a standard deviation of 0.05 cm

a) If we use 45 randomly selected rings and calculate the sample mean, what is the probability of having a sample mean greater than 12.00cm? (use original value of standard deviation)

b) Assume you take 39 rings and put them side by side in a line, touching each other like this "OOOO..." what is the probability that the length of the line will exceed 489cm? (use original value of standard deviation)

Answer 1

Note- probabilities are obtained from Z table

. let x diameter of cument piston rings (cm) Xu Nonnal ( U=11, r=0.05 ) lut mean X = Sample Ex= total length Using central limit thorem xn Normal Cloolin) Exu Normal (nl. sin ) i probe x > 12 for n= 45 Requind probability is P[ X >12] =pl X-M > 12-11 0.05/45 =P [ z> 134] z 0.0000 ✓ P[ Exi 489 ] For n=39 = P {zxinu z Plexi-nly > 489 -3x) 0.05 39 P[z > 192.1538] IN 0.0000 ✓ 01