Question

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 it is an unusually dry year? Why or why not?

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

Answer #1

Problem 5. The mean yearly rainfall in Sydney,
Australia, is 136.9 mmand 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 it is an unusually...

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. The annual rainfall is normally distributed with mean = 40.14
inches and standard deviation 8.7 inches.
a) What is the probability this years’ rainfall will exceed 42
inches?
b) What is the probability that the sum of the next two years’
rainfall will exceed 84 inches?

The mean annual rainfall in a particular region is 80
inches with a standard deviation of 8 inches. If a sample of 32
years is selected, what is the probability that the mean annual
rainfall for this sample will be less than 79 inches?

The lengths of adult males' hands are normally distributed with
mean 186 mm and standard deviation is 7.3 mm. Suppose that 10
individuals are randomly chosen. Round all answers to 4 where
possible.
For the group of 10, find the probability that the average hand
length is less than 187.
Find the first quartile for the average adult male hand length
for this sample size.

The time taken for a standard flight from Melbourne to Sydney is
normally distributed with a mean of 75mins and a standard deviation
of 7mins.
a) What is the probability of a flight taking longer than
80mins?
b) If there are 500 flights from Melbourne to sydney each week, how
many of these will take more than 80mins?

The lengths of adult males' hands are normally distributed with
mean 190 mm and standard deviation is 7 mm. Suppose that 48
individuals are randomly chosen. Round all answers to 4 where
possible.
For the group of 48, find the probability that the average hand
length is less than 192.
Find the third quartile for the average adult male hand length
for this sample size.
For part b), is the assumption that the distribution is normal
necessary?

The lengths of adult males' hands are normally distributed with
mean 195 mm and standard deviation is 7.1 mm. Suppose that 49
individuals are randomly chosen. Round all answers to 4 where
possible. What is the distribution of ¯ x ? ¯ x ~ N( , ) For the
group of 49, find the probability that the average hand length is
more than 196. Find the first quartile for the average adult male
hand length for this sample size. For...

The lengths of adult males' hands are normally distributed with
mean 186 mm and standard deviation is 7 mm. Suppose that 9
individuals are randomly chosen. Round all answers to 4 where
possible.
A. What is the distribution of ¯x? ¯x ~
N( , )
B. For the group of 9, find the probability that the average
hand length is more than 184.
C. Find the first quartile for the average adult male hand
length for this sample size.
D....

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