Question

I totally forgot how to find a z-score. Please help and explain.

Answer 1

Just a simple review:

Z(X)= (X-mean)/standard deviation=(X- μ ) / σ

Given:

μ = 180

&sigmal = 8

Z(196)=(196-180)/8 = 2

Here, we're looking for the right tail, i.e. for Z scores greater than 2.

The table gives the area (probability) under the normal curve from Z(0) to Z(X).

Thus for estmating probability for the right tail, we subtract the Z-score from 0.5.

The value of probability where

P(0<Z<2)=0.4772

P(Z>2.0) = 0.5-0.4772 = 0.0228

Therefore the probability of box weghing more than 196 oz is 0.0228, 0r 2.28%.

Answer 2

The z-score is the number of standard deviations from the mean. For a given x-value, mean (μ), and standard deviation (σ) the z-score is given by

... z = (x -μ)/σ

(a) x=196, μ = 180, σ = 8 gives a z-score of

... z = (196 -180)/8 = 16/8

... z = 2.0

(b) The area associated with x=2 is 0.4772

(c) Rounded to the nearest thousandth, this is 0.477

(d) Carl's subtraction gives

... 0.50 - 0.477 = 2.3%