Question

The time it takes to assemble a component on a factory assemble line is normally distributed with a man of 3.1 minutes and a standard deviation of 0.6 minutes. Find the probability that a randomly selected employee will take between 2.0 and 2.3 minutes? Answer In a Sentence Question 7: The following data gives the information of the number of children that could complete an activity in the specified time. Construct a histogram with probabilities. Time No. of Children 30 40 25 20 53 Question 8 The mean weight of a cereal box filled by a machine is 15.0 oz with a standard deviation of .4 oz. If the weights of all the boxes filled by the machine are normally distributed, what, what percent of the boxes will weigh between 14.5 and 16.2 oz? Answer In a Sentence:

Answer 1

Let X be a random variable which takes the time to assemble a component on a factory assemble line.

Therefore X follows normal distribution with mean = $\mu$ = 3.1 minutes and standard deviation = $\sigma$ = 0.6 minutes.

Here we want to find P( 2.0 < X < 2.3) = P( X < 2.3 ) - P(X < 2.0) .......( 1 ).

Let's use excel:

P( X < 2.3 ) = "=NORMDIST(2.3,3.1,0.6,1)" = 0.0912

P( X < 2.0 ) = "=NORMDIST(2.0,3.1,0.6,1)" = 0.0334

Plug these values in equation ( 1 ), we get:

P( 2.0 < X < 2.3) =  0.0912 -  0.0334 = 0.0578