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5.2: the uniform distribution

47 . For the continuous probability distribution described by the function f ( x ) = 1 10 for 0 x 10 , what is the P (2< x <5)?

Use the following information to answer the next four exercises. The number of minutes that a patient waits at a medical clinic to see a doctor is represented by a uniform distribution between zero and 30 minutes, inclusive.

48 . If X equals the number of minutes a person waits, what is the distribution of X ?

49 . Write the probability density function for this distribution.

50 . What is the mean and standard deviation for waiting time?

51 . What is the probability that a patient waits less than ten minutes?

5.3: the exponential distribution

52 . The distribution of the variable X , representing the average time to failure for an automobile battery, can be written as: X ~ Exp ( m ). Describe this distribution in words.

53 . If the value of m for an exponential distribution is ten, what are the mean and standard deviation for the distribution?

54 . Write the probability density function for a variable distributed as: X ~ Exp (0.2).

6.1: the standard normal distribution

55 . Translate this statement about the distribution of a random variable X into words: X ~ (100, 15).

56 . If the variable X has the standard normal distribution, express this symbolically.

Use the following information for the next six exercises. According to the World Health Organization, distribution of height in centimeters for girls aged five years and no months has the distribution: X ~ N (109, 4.5).

57 . What is the z -score for a height of 112 inches?

58 . What is the z -score for a height of 100 centimeters?

59 . Find the z -score for a height of 105 centimeters and explain what that means In the context of the population.

60 . What height corresponds to a z -score of 1.5 in this population?

61 . Using the empirical rule, we expect about 68 percent of the values in a normal distribution to lie within one standard deviation above or below the mean. What does this mean, in terms of a specific range of values, for this distribution?

62 . Using the empirical rule, about what percent of heights in this distribution do you expect to be between 95.5 cm and 122.5 cm?

6.2: using the normal distribution

Use the following information to answer the next four exercises. The distributor of lotto tickets claims that 20 percent of the tickets are winners. You draw a sample of 500 tickets to test this proposition.

63 . Can you use the normal approximation to the binomial for your calculations? Why or why not.

64 . What are the expected mean and standard deviation for your sample, assuming the distributor’s claim is true?

65 . What is the probability that your sample will have a mean greater than 100?

66 . If the z -score for your sample result is –2.00, explain what this means, using the empirical rule.

7.1: the central limit theorem for sample means (averages)

67 . What does the central limit theorem state with regard to the distribution of sample means?

68 . The distribution of results from flipping a fair coin is uniform: heads and tails are equally likely on any flip, and over a large number of trials, you expect about the same number of heads and tails. Yet if you conduct a study by flipping 30 coins and recording the number of heads, and repeat this 100 times, the distribution of the mean number of heads will be approximately normal. How is this possible?

Questions & Answers

What is nominal variable
olusola Reply
Write short notes on, nominal variable, ordinal variable, internal variable, ratio variable.
olusola
P( /x-50/ less than or equal to 5 ) where mean =52 and Variance =25
Jay Reply
how I get the mcq
Mukesh Reply
please what is data mining
Josephine Reply
the exploration and analysis of large data to discover meaningful patterns and rules
Hussein
how do we calculate the median
All Reply
f(x)=cx(1-x)^4 as x range 4rm 0<=x<=1. Can someone pls help me find d constant C. By integration only..
Akeem Reply
uses of statistics in Local Government
Saleema Reply
Hi
Tamuno
hello
Saleema
state road transport corporation
Atul
District statistical officer
Atul
statistical services
Atul
Please is this part of the IMT program
Tamuno
testing of drugs
Shambhavi
hii 2
Qamar-ul-
How about population census
Tamuno
Hello every one
Okoi
sample survey is done by local government in each and every field.
syeda
statistics is used in almost every government organisations such as health department, economic department, census, weather forecasting fields
raghavendra
that's true
syeda
statistics is one of the tool that represents the falling and rising of any cases in one sheet either that is in population census whether forecast as well as economic growth
Aadil
statistic is a technique, and statistics is a subject
syeda
what is business statistics
PM Reply
Probability tells you the likelihood of an event happening. ... The higher the probability, the more likely it is to happen. Probability is a number or fraction between 0 and 1. A probability of 1 means something will always happen, and a probability of 0 means something will never happen...
La Reply
Saying it's a number between zero and one means it is a fraction so you could remove "or fraction" from you definition.
Carlos
wouldn't be correct to remove fractions, saying a number is justified as probabilities can also be decimals between 0 and 1.
Denzel
Saying "a number" will include it being a decimal which are themselves fractions in another form.
Carlos
I will simply say a probability is a number in the range zero to one, inclusive.
Carlos
f#$
Carlos
How to delete an entry? This last one was a pocket print.
Carlos
what is probability
sky-D Reply
what is data
Muhd Reply
What is Statistic
ibrahim Reply
what statistical analysis can i run on growth and yield of spinach.
guillio
format of the frequency distribution table
henry
what is pearson correlation coefficient indicates?
Eticha
Statistic is the mean of the sample.
Raman
can anyone determine the value of c and the covariance and correlation for the joint probability density function Fxy(x,y)=c over the range 0<x<5,0<y,and x-1<y<x-1.
Nuhu
what actually is the definition of range
Chinedu Reply
I need social statistics materials
Chinedu
the range of a set of data is the difference between the largest and smallest values
La
I need more explanation about cluster sampling
Hafsat
write the set of old number that are greater than or equal to minutes 7 butl less than 5 in both of the set notation
Jerry Reply
What is the formula for iqr
Erin Reply
Q3-Q1
Sk
which is 3rd quartile minus 1st quartile.
Sk
hope that will help you.
Sk

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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