Question

7. The dimension of a machined part made by Machinheimer Machinery has a nominal specification of 11.9 cm. The process that produces the part can be controlled to have a mean value equal to this specification, but has a standard deviation of 0.05 cm. What is the probability that a part will have a dimension: a. exceeding 12 cm? b. between 11.9 and 11.95 cm? c. less than 11.83 cm?

Answer 1

Solution:

a)

P(x > 12) = 1 - P(x < 12)

= 1 - P((x - ) / < (12 - 11.9) / 0.05)

= 1 - P(z < 2)

= 1 - 0.9772 Using standard normal table.

= 0.0228

Probability = 0.0228

b)

P(11.9 < x < 11.95) = P((11.9 - 11.9)/ 0.05) < (x - ) /  < (11.95 - 11.9) / 0.05) )

= P(0 < z < 1)

= P(z < 1) - P(z < 0)

= 0.8413 - 0.5000 Using standard normal table,  

Probability = 0.3413

c)

P(x < 11.83) = P((x - ) / < (11.83 - 11.9) / 0.05)

= P(z < -1.4)

= 0.0808 Using standard normal table,

Probability = 0.0808