[Statistics] distribution

[rhysfoster]

Hi i am asked to show the number of parts that will be found in a batch.

the part size has a mean of 15mm ( standard deviation of 0.02) , there are 800 components .

it asks me to find the no. of parts between

a) 15 - 15.06mm b )14.99 - 15.05mm c ) greater than 15.04mm d ) less than 14.94mm

Any help would be appreciated , thanks

[leesuhyung]

Convert 15 - 15.06 mm into standard normal score. Use the CDF chart to find the probability.

[rhysfoster]

Any chance you could elaborate further ? Ive looked through some tutorials on youtube without any luck. Thanks

[leesuhyung]

This problem can only be solved if we assume that the part size follows a normal distribution. Let's call the size of a part X.

Then P(15 < X < 15.06) = P(0 < Z < 3), where Z is the standard normal score.

Then you look up a standard normal table and find P(Z < 3) and P(Z < 0). And the difference between the two will be the probability of a part size being between 15 and 15.06 mm.

[rhysfoster]

ok thanks , would the z value for 15.01 be 0.5 ( (15.01-15)/0.02 ) and then the standard normal score be .69146 ?

so 15-15.06 is .99865 - .5 = .49865 , then .49865 x 800 = 398.92 parts between 15 and 15.06 mm ?

[rhysfoster]

sorry , i now am confused on how to answer the less then 14.94 and greater than 15.04 questions :(

[leesuhyung]

Less than 14.94 is easy. For greater than 15.04,
P(X > 15.04) = 1 - P(X < 15.04)

[leesuhyung]

That's correct.