Statistics I. International Group Departamento de Economa Aplicada Universitat de Valncia

May 20, 2010

Problem 35

Random variable X : weekly ticket sales (units) of a museum. X ∼ N(1000, 180)

Find the probability of weekly sales exceeding 850 tickets. Find the probability of the interval 1000 to 1200 Take 5 weeks at random. Find the probability of weekly sales not exceeding 850 tickets in more than two weeks Ticket price is 4.5 Euros. Deﬁne the distribution of weekly revenue

Problem 35 (a)

Random variable X : weekly ticket sales (units) of a museum. X ∼ N(1000, 180) Find the probability of weekly sales exceeding 850 tickets. Find the probability of the interval 1000 to 1200 P(X > 850)? P(X > 850) = P(Z > 850 − 1000 ) = P(Z > −0.83) = 180

P(Z < 0.83) = P(Z < 0.83) = 0.7967

Problem 35 (a)
Random variable X : weekly ticket sales (units) of a museum. X ∼ N(1000, 180) Find the probability of weekly sales exceeding 850 tickets. Find the probability of the interval 1000 to 1200 P(1000 < X < 1200)? P(1000 < X < 1200) = P(X < 1200) − P(X < 1000) = 1200 − 1000 1000 − 1000 ) − P(Z < ) 180 180 = P(Z > −0.83) = P(Z < 1.11)−P(Z < 0) = 0.8665−0.5 = P(Z < = 0.3665

Problem 35 (b)
Probability of more than two weeks with sales not exceeding 850 tickets Y : number of weeks with sales not exceeding 850 tickets in 5 weeks. The probability of sales being less than 850 tickets (found in the ﬁrst section) is 1-0.7967=0.2033. Let us analyze this random experiment Ticket sales for one week can be below or above 850 (success/failure) We repeat the previous step n = 5 trials Then the number of weeks with ticket sales below 850 in 5 trials, variable Y , follows a binomial distribution Y ∼ Bi(p = 0.2033, n = 5)

Problem 35 (b)

Probability of more than two weeks with sales not exceeding 850 tickets Y ∼ Bi(p = 0.2033, n = 5)

...NORMALDISTRIBUTION
1. Find the
distribution:
a.
b.
c.
d.
e.
f.
following probabilities, the random variable Z has standard normal
P (0< Z < 1.43)
P (0.11 < Z < 1.98)
P (-0.39 < Z < 1.22)
P (Z < 0.92)
P (Z > -1.78)
P (Z < -2.08)
2. Determine the areas under the standard normal curve between –z and +z:
♦ z = 0.5
♦ z = 2.0
Find the two values of z in standard normaldistribution so that:
P(-z < Z...

...standard deviation = square root of variance = sqrt(846) = 29.086 4. If we have the following data
34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66 Draw a stem and leaf. Discuss the shape of the distribution. Solution: 2 3 4 5 6 | | | | | 219200 48714 0197 6
This distribution is right skewed (positively skewed) because the “tail” extends to the right. 5. What type of relationship is shown by this scatter plot?
45 40 35 30 25 20 15 10 5 0 0 5...

...decimal places)
2. Find the value of z if the area under a Standard Normal curve
a) to the right of z is 0.3632;
b) to the left of z is 0.1131;
c) between 0 and z, with z > 0, is 0.4838;
d) between -z and z, with z > 0, is 0.9500.
Ans : a) z = + 0.35 ( find 0.5- 0.3632 = 0.1368 in the normal table)
b) z = -1.21 ( find 0.5 – 0.1131 = 0.3869 in the normal table)
c ) the area between 0 to...

...Pages
C H A P T E
R
6
The NormalDistribution
Objectives
Outline
After completing this chapter, you should be able to
1
2
3
Identify distributions as symmetric or skewed.
4
Find probabilities for a normally distributed
variable by transforming it into a standard
normal variable.
Introduction
6–1
NormalDistributions
Identify the properties of a...

...
NormalDistribution
Student’s Name:
Instructorr:
Date ofSubmission:
The table 1 below shows a relationship between actual daily temperatures and precipitation in the month of January 2011. These data was adopted from a meterological station in the states of Alaska, in the United States. Normal distributed data aresymmetric with a single bell shaped peaks. Th maean of the data it significant in...

...200 or so people. The rehabilitation center is a nice thought, but the fact that a 13 million dollar a year revenue charity can only build one rehabilitation center in the 7 years that the LRA has moved to South Sudan just highlights the inherent problem of IC being based in Uganda.
Works Cited
1. Josiah. "Concerning KONY 2012 - Nothing Suspicious Going On Here." Nothing Suspicious Going On Here. 7 Mar. 2012. Web. 13 Mar. 2012. .
2. Manhire, Toby. "Kony 2012:...

...computer at school or the office, and finish on
your home computer. Never email yourself a file again!
The Dropbox Folder
After you install Dropbox on your computer, a Dropbox folder is created. If you’re reading this guide,
then that means you had no problems finding your Dropbox folder :). This folder is just like any other
folder on your computer, but with a twist. Any file you save to your Dropbox folder is also saved to all
your other computers, phones, and the Dropbox...

...
NormalDistributionNormaldistribution is a statistics, which have been widely applied of all mathematical concepts, among large number of statisticians. Abraham de Moivre, an 18th century statistician and consultant to gamblers, noticed that as the number of events (N) increased, the distribution approached, forming a very smooth curve.
He insisted that a new discovery of a...