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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

the mean of random variable following binomial distribution is 10. the numbers of trails are 30. What the approximate value of variance?
AMIT Reply
what is chis square
Remelyn Reply
A chi-square (χ2) statistic is a test that measures how a model compares to actual observed data.
kalim
descriptive statistics basic
Sangeetha
Hi Friends
Sangeetha
tamil people yaaraavathu irukkingala
Sangeetha
what is the median of the following set of number:3,3,3,4,5,6,7,8,8,9?
Sur Reply
3
Mbemah
5.6
Alekya
(5+6)/2=5.5555.......=5.6
Lyrical
(5+6)/2=5.5 that is the median
moniba
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nathan
hi friends am new here, hope am welcome
nathan
1.5
nathan
differences between Intervals and Ratio measurement scales
VIP Reply
interval is the distinct from a starting point to the peak of a certain distance
Mbemah
the taking of a certain range accurately in a divisional way
Mbemah
i need the solution for exercise sums
Siva Reply
descriptive statistics sums I need
Sangeetha
statistics discovered?
Kaleem Reply
internet
Kamranali
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Virendra
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Nija
purpose of of statistics
mukesh
ya..
mukesh
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Sangeetha
Odisha ru kau bhai mane achha?
Hemanta
I want to learn my MSC by statistics who can help me ?
Abebe
@Avirup interest person
Abebe
good morning
Sangeetha
Dr good morning
mukhtar
in statistical inferences we use population parameter to infer sample statistics
anupama Reply
Yes
lukman
how do we calculate decile
Drix Reply
how do we calculate class boundaries
Syed
The lower class boundary is found by subtracting 0.5 units from the lowerclass limit and the upper class boundary is found by adding 0.5 units to the upper class limit. The difference between the upper and lowerboundaries of any class.
Ekene
The lower class boundary is found by subtracting 0.5 units from the lowerclass limit and the upper class boundary is found by adding 0.5 units to the upper class limit. The difference between the upper and lowerboundaries of any class.
Ekene
complete definition plz
Zarifa Reply
what are the advantages and disadvantages of primary and secondary data
Elisha Reply
the average increase for all NASDAQ stocks is the
Technical Reply
formula of poisson probability distribution
Ch Reply
frequency distribution table
Ali Reply
Giveanswer
Girma
sum of dots when 2 dice are rolled is
Babra Reply
what is statistics?
Noman Reply
Statistics is the collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions.
John
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razia
you are right
razia

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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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