Question

A manufacturing process outputs parts having a normal distribution with a mean of 30 cm and standard deviation of 2 cm. From a production sample of 80 parts, what proportion of the sample can be expected to fall between 28 and 32 cm? (ref Activity 7.16)

Group of answer choices

68%

50%

95%

90%

Answer 1

Solution :

Given that,

mean = = 30

standard deviation = = 2

P (28 < x < 32 )

P ( 28 - 30 / 2 < ( - /) < ( 32 - 30 / 2 )

P ( - 2 / 2 < z < 2 / 2)

P (-1 < z < 1 )

P ( z < 1 ) - P ( z < -1)

Using z table

= 0.8413 - 0.1587

= 0.6826

Probability = 0.6826 = 68%