Include all work in a neat and well organized presentation plz. There are two ma
ID: 3252049 • Letter: I
Question
Include all work in a neat and well organized presentation plz.
There are two machines available for cutting corks intended for use in wine bottles. The first machine produces corks with diameters that are normally distributed with a mean of 3 cm and a standard deviation of .1 cm. The second machine produces corks with diameters that are normally distributed with a mean of 3.04 cm and a standard deviation of .02 cm. Acceptable corks have diameters between 2.9 cm to 3.1 cm. Which machine is more likely to produce an acceptable cork?Explanation / Answer
P(X < A) = P(Z < (A - mean)/standard deviation
Considewr the first machine,
P(2.9 < X < 3.1) = P(X < 3.1) - P(X < 2.9)
= P(Z < (3.1 - 3)/0.1) - P(Z < (2.9 - 3)/0.1)
= P(Z < 1) - P(Z < -1)
= 0.8413 - 0.1587
= 0.6826
Consider second machine,
P(2.9 < X < 3.1) = P(X < 3.1) - P(X < 2.9)
= P(Z < (3.1 - 3.04)/0.02) - P(Z < (2.9 - 3.04)/0.02)
= P(Z < 3) - P(Z < -7)
= 0.9987 - 0
= 0.9987
So, the second machine is more likely to produce an acceptable cork