Question

In: Statistics and Probability

Samples of 36 parts are taken from a manufacturing process that produces machine parts with a...

Samples of 36 parts are taken from a manufacturing process that produces machine parts with a mean diameter of 12.40 cm and a standard deviation of 0.06 cm. If the diameters are normally distributed, what proportion of sample means will have diameters between 12.39 and 12.41 cm?

Expert Solution

Solution :

Given that ,

mean = = 12.40

standard deviation = =0.06

n = 36

= 12.40

= / $\sqrt$ n= 0.06 / $\sqrt$ 36=0.01

P(12.39< < 12.41) = P[(12.39-12.40) / 0.01< ( - ) / < (12.41-12.40) / 0.01)]

= P( -1< Z <1 )

= P(Z <1 ) - P(Z < -1)

Using z table

=0.8413 - 0.1587

=0.6826

probability= 0.6826

orchestra answered 3 years ago

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