220 Fundamentals of Statistics
b. If you collect 25 years of accident in-
formation at this factory, how could
the number of accidents per year be
used to estimate x? What would be
the standard error of this estimate?- Excel includes a function to calculate
values of the Poisson distribution. The
syntax of the function is
POISSON(x, mean, cumulative)where x is the number of counts, mean
is the expected number of counts, and
cumulative is TRUE to calculate the cu-
mulative value of the probability function
and FALSE to calculate the density for
the specifi ed x value. Use this function
to calculate the cumulative and specifi c
probabilities of the following values:
a. l 5 2, x 52
b. l 5 2, x 53
c. l 5 2, x 54
d. l 5 2, x 55
- Excel includes a function to calculate
the probabilities associated with the
standard normal distribution. The syn-
tax of the function is
NORMSDIST(z)The function returns the probability of a
standard normal random variable having
a value ≤ z. Use this function to calcu-
late the following probabilities:
a. z 5 .5
b. z 5 1
c. z 5 1.65
d. z 5 1.96
e. What is the probability of a standard
normal random variable having a
value of exactly 2.0?
- The Excel function
NORMSINV(prob)returns the inverse of the standard
normal distribution. For a given
cumulative probability prob, the func-
tion returns the value of z. Use this
function to calculate z values for the
following probabilities of the standard
normal distribution:
a. .05
b. .10
c. .50
d. .90
e. .95
f. .975
g. .99- Excel includes a function to calculate
the probability for a random variable
coming from any normal distribution.
The syntax of the function is
NORMDIST(x, mean, std_dev,
cumulative)
where x is the value of the random vari-
able, mean is the mean of the normal
distribution, std_dev is the standard
deviation of the distribution, and
cumulative is TRUE to calculate the
cumulative value of the probability
function and FALSE to calculate the
pdf for the specified x value. Use this
function to calculate the cumulative
probabilities for the following values:
a. x 5 1.96, mean 5 0, std_dev 5 1
b. x 5 1.96, mean 5 0, std_dev 5 0.5
c. x 5 1.96, mean 5 0, std_dev 5 0.25
d. x 5 2 1.96, mean 5 0, std_dev 5 1
e. x 5 5, mean 5 5, std_dev 5 2- The Excel function
NORMINV(prob, mean, std_dev)
calculates the inverse of the normal
distribution. For a cumulative prob-
ability of prob, a mean value of mean,
and a standard deviation of std_dev, the