7.9.1 Find the z-score (the number of standard
deviations from the mean) for the following measurements. A value of
11.0 drawn from a normal distribution with mean 13.0 and standard
deviation 1.2.
Get solution
7.9.2 Find the z-score
(the number of standard deviations from the mean) for the following
measurements. A value of 0.9 drawn from a normal distribution with mean
0.5 and standard deviation 0.3.
Get solution
7.9.3 Find the z-score
(the number of standard deviations from the mean) for the following
measurements. A value of 12.0 drawn from a normal distribution with
mean 10.0 and variance 25.0.
Get solution
7.9.4 Find the z-score
(the number of standard deviations from the mean) for the following
measurements. A value of 7.0 drawn from a normal distribution with mean
10.0 and variance 4.0.
Get solution
7.9.5 Use the cumulative distribution function for the standard normal, Φ (z),
to find the following probabilities. Shade the associated area on two
graphs: the given normal distribution, and the standard normal
distribution. The probability of a value less than 0.7 drawn from a normal distribution with mean 0 and variance 1.
Get solution
7.9.6 Use the cumulative distribution function for the standard normal, Φ (z),
to find the following probabilities. Shade the associated area on two
graphs: the given normal distribution, and the standard normal
distribution. The probability of a value greater than −0.1 drawn from a normal distribution with mean 0 and variance 1.
Get solution
7.9.7 Use the cumulative distribution function for the standard normal, Φ (z),
to find the following probabilities. Shade the associated area on two
graphs: the given normal distribution, and the standard normal
distribution. The probability of a value greater than 11.0 drawn
from a normal distribution with mean 13.0 and standard deviation 1.2
(as in Exercise 1).
Get solution
7.9.8 Use the cumulative distribution function for the standard normal, Φ (z),
to find the following probabilities. Shade the associated area on two
graphs: the given normal distribution, and the standard normal
distribution. The probability of a value less than 0.9 drawn
from a normal distribution with mean 0.5 and standard deviation 0.3(as
in Exercise 2).
Get solution
7.9.9 Use the cumulative distribution function for the standard normal, Φ (z),
to find the following probabilities. Shade the associated area on two
graphs: the given normal distribution, and the standard normal
distribution. The probability of a value between 10.0 and 12.0
drawn from a normal distribution with mean 10.0 and variance 25.0 (as in
Exercise 3).
Get solution
7.9.10 Use the cumulative distribution function for the standard normal, Φ (z),
to find the following probabilities. Shade the associated area on two
graphs: the given normal distribution, and the standard normal
distribution. The probability of a value between 7.0 and 13.0
drawn from a normal distribution with mean 10.0 and variance 4.0 (as in
Exercise 4).
Get solution
7.9.11 Using
a table or computer program that can calculate the cumulative
distribution function for the standard normal, find the following
probabilities. The masses of a type of insect are normally
distributed with a mean of 0.38 g and a standard deviation of 0.09 g.
What is the probability that a given insect has mass less than 0.40 g?
Get solution
7.9.12 Using
a table or computer program that can calculate the cumulative
distribution function for the standard normal, find the following
probabilities. Scores on a test are normally distributed with
mean 70 and standard deviation 10. What is the probability that a
student scores more than 85?
Get solution
7.9.13 Using
a table or computer program that can calculate the cumulative
distribution function for the standard normal, find the following
probabilities. Measurement errors are normally distributed with a
mean of 0 mm and a standard deviation of 0.01 mm. Find the probability
that a given measurement is within 0.012 mm of the true value.
Get solution
7.9.14 Using
a table or computer program that can calculate the cumulative
distribution function for the standard normal, find the following
probabilities. The number of insects captured in a trap on
different nights is normally distributed with mean 2950 and standard
deviation 550. What is the probability of capturing between 2500 and
3500 insects?
Get solution
