Question

#17

of a certain steel washer. What is the expected number of process cycles before the washer fails? 17 A company manufactures concrete blocks that are used for construction purposes. Suppose that the individual concrete blocks are normally distributed with a mean weight of 11 kg and a standard deviation of 0.3 kg. Determine the probability that a concrete block weighs between the tolerances of 10.9+ 2 kg.

Answer 1

Given,

$\mu$ = 11 , $\sigma$ = 0.3

We convert this to standard normal as

P(X < x) = P(Z < x - $\mu$ / $\sigma$ )

So,

P(10.9 - 0.2 < $\bar{x}$ < 10.9 + 0.2) = P($\bar{x}$ < 10.9+0.2) - P( $\bar{x}$ < 10.9 - 0.2)

= P($\bar{x}$ < 11.1) - P($\bar{x}$ < 10.7)

= P(Z < (11.1 - 11) / 0.3) - P(Z < (10.7 - 11) / 0.3 )

= P(Z < 0.33) - P(Z < -1)

= 0.6293 - 0.1587

= 0.4706