Question

**Problem 5**. The mean yearly rainfall in Sydney,
Australia, is ** 136.9 mm**and the standard
deviation is

**(a)**What is the random variable?

**(b)**Find the probability that the yearly
rainfall is less than 100 mm.

**(c)**Find the probability that the yearly
rainfall is more than 240 mm.

**(d)**Find the probability that the yearly
rainfall is between 140 and 250 mm.

**(e)**If a year has a rainfall less than 100mm,
does that mean it is an unusually dry year? Why or why
not?

**(f)**What rainfall amount are 90% of all yearly
rainfalls more than?

Answer #1

The mean yearly rainfall in Sydney, Australia, is 136.9 mm and
the standard deviation is 69.4mm. Assume rainfall is normally
distributed.
(a) What is the random variable?
(b) Find the probability that the yearly rainfall is less than
100 mm.
(c) Find the probability that the yearly rainfall is more than
240 mm.
(d) Find the probability that the yearly rainfall is between 140
and 250 mm.
(e) If a year has a rainfall less than 100mm, does that mean...

The mean yearly rainfall in Sydney, Australia, is about 134 mm
and the standard deviation is about 66 mm ("Annual maximums of,"
2013). Assume rainfall is normally distributed. How many yearly mm
of rainfall would there be in the top 15%? Round answer to 2
decimal places. Answer:

6.4.4
Annual rainfalls for Sydney, Australia are given in table
#6.4.6. ("Annual maximums of," 2013). Can you assume rainfall is
normally distributed?
Table #6.4.6: Annual Rainfall
in Sydney, Australia
146.8
383
90.9
178.1
267.5
95.5
156.5
180
90.9
139.7
200.2
171.7
187.2
184.9
70.1
58
84.1
55.6
133.1
271.8
135.9
71.9
99.4
110.6
47.5
97.8
122.7
58.4
154.4
173.7
118.8
88
84.6
171.5
254.3
185.9
137.2
138.9
96.2
85
45.2
74.7
264.9
113.8
133.4
68.1
156.4
6.5.2
A random variable...

1) X is normally distributed with a mean of 60 and a standard
deviation of 12.
a) Find the probability that X is less than 42
b) Find the probability that X is more than 70.
2) Weights of Yellow Labradors are normally distributed with
a mean of 55 pounds and a standard
deviation of 6.2 pounds. What proportion of Yellow Labradors
weigh between 50 and 60 pounds?

A dishwasher has a mean life of 12 years with an estimated
standard deviation of 1.25 years ("Appliance life expectancy,"
2013). Assume the life of a dishwasher is normally distributed.
State the random variable.
Find the probability that a dishwasher will last more than 15
years.
Find the probability that a dishwasher will last less than 6
years.
Find the probability that a dishwasher will last between 8 and
10 years.
If you found a dishwasher that lasted less than...

A dishwasher has a mean life of 12 years with an estimated
standard deviation of 1.25 years ("Appliance life expectancy,"
2013). Assume the life of a dishwasher is normally distributed. a.)
State the random variable. b.) Find the probability that a
dishwasher will last more than 15 years. c.) Find the probability
that a dishwasher will last less than 6 years. d.) Find the
probability that a dishwasher will last between 8 and 10 years. e.)
If you found a...

A dishwasher has a mean life of 10 years with an estimated
standard deviation of 1.05 years ("Appliance life expectancy,"
2013). The life of a dishwasher is normally distributed. Suppose
you are a manufacturer and you take a sample of 10 dishwashers that
you made.
State the random variable.
Find the mean of the sample mean.
Find the standard deviation of the sample mean.
What is the shape of the sampling distribution of the sample
mean? Why?
Find the probability...

A dishwasher has a mean life of 12 years with an estimated
standard deviation of 1.25 years ("Appliance life expectancy,"
2013). The life of a dishwasher is normally distributed. Suppose
you are a manufacturer and you take a sample of 10 dishwashers that
you made.
State the random variable.
Find the mean of the sample mean.
Find the standard deviation of the sample mean.
What is the shape of the sampling distribution of the sample
mean? Why?
Find the probability...

A dishwasher has a mean life of 12 years with an estimated
standard deviation of 1.25 years ("Appliance life expectancy,"
2013). The life of a dishwasher is normally distributed. Suppose
you are a manufacturer and you take a sample of 10 dishwashers that
you made.
State the random variable.
Find the mean of the sample mean.
Find the standard deviation of the sample mean.
What is the shape of the sampling distribution of the sample
mean? Why?
Find the probability...

A dishwasher has a mean life of 12 years with an estimated
standard deviation of 1.25 years ("Appliance life expectancy,"
2013). The life of a dishwasher is normally distributed. Suppose
you are a manufacturer and you take a sample of 10 dishwashers that
you made. a.) State the random variable. b.) Find the mean of the
sample mean. c.) Find the standard deviation of the sample mean.
d.) What is the shape of the sampling distribution of the sample
mean?...

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