6.2
a pizza parlor: mean= 8 ounces standard deviaiton= 0.5 ounces picks out a large pizza at random, finds made up of 6.9 ounces of cheese; amount of cheese on pizza is a normal distribution how many standard deviations from the mean is 6.9?
-2.20 meaning, the amont of cheese is 2.20 standard devioations below the mean
fawn weighs 14 kg, is it an unusually small animal? mean= 27.4 standard deiation= 3.4 kg
...
let z be a random variable with a standard normal distribution. find the indicated probability. P(z less than or equal to -0.29)
.3859
mean of original distribution in standard units is
0
what is the value of the standard score for the mean of a distribution
0
the z distribution, in a normal distribution has a mean of .... and a standard deviation of ....
0 1
let z be a random variable with a standard normal distribution. find the probability. P(Z greater than or equal to 1.96)
0.0250
find indicated probability: P(-0.40 <|z|> 2.08
0.6366
2 conventions for the table
1. any area to the left of z value smaller than -3.49 as 0 2. treat any area to the right of z value greater than 3.49 as 1.000
Rod: mean: 17 minutes standard deviation= 3 minutes -took him 21 minutes to get to class; how many standard deviations from the average? -what commuting time corresponds to standard score of z=-2.5?
1.33 9.5 minutes
any normal distribution can be converted to the standard normal distribution
by converting all x values to their corresponding z values
if the original distribution of x values is normal, then the
corresponding z values have a normal distribution as well
how these types of questions will be formualted- ones with z values whose probabilities need to be taken from the table
let z be a random variable with a standard normal distribution
what are the values of the mean and standard deviation of a standard normal distribution?
mean= 0 standard deviation= 1
each area is equal to the
probability that the measurement of that item falls in this interval
what about a raw score greate rthan a mean? in relation to standard scores
raw scores above the mean will have positive standard scores
does a raw score less than the mean equal positive or negative standard score?
raw scores less than the mean will have negative standard scores
z value gives the number of
standard deviations between the original x and the mean of the x distribution
the z values on the ________ _____ ______ have _____ beyond for their value
standard normal distribution; area
what can help find the area under the standard normal curve?
the standard normal distribution
given an .... distribution with a mean and standard deviation, what can one find?
x; raw score x corresponding to a z score
if a z value is negative, is the area to the left of z less than 0.5?
yes
if a z value is positive, is the area to the left of z greater than 0.5?
yes
as z values increase, do areas to the left of z increase?
yes,
x value below the mean has
a negative z value
the standard normal distribution is
a normal distribution with mean 0 and standard deviation 1
an x value in the original distribution above the mean has
a z value that is positive