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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

Write a short note on skewness
Saran Reply
and on kurtosis too
Hiren
What is events
Manish Reply
who is a strong man?
Desmond Reply
Can you sir plz provide all the multiple choice questions related to Index numbers.?
Hiren Reply
about probabilty i have some questions and i want the solution
asad Reply
What is hypothesis?
Rosendo Reply
its a scientific guess
ted
A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon. In a scientific experiment or study, the hypothesis is a brief summation of the researcher's prediction of the study's findings.
Hamzah
Which may be supported or not by the outcome. Hypothesis testing is the core of the scientific method.
Hamzah
statistics means interpretation analysis and representation of numerical data
Ramzan
To check the statment or assumption about population parameter is xalled hypothesis
Ali
hypothesis is simply an assumption
Patrick
what is the d.f we know that how to find but basically my question is what is the d.f? any concept please
asad Reply
Degrees of freedom aren’t easy to explain. They come up in many different contexts in statistics—some advanced and complicated. In mathematics, they're technically defined as the dimension of the domain of a random vector.
Hamzah
d.f >> Degrees of freedom aren’t easy to explain. They come up in many different contexts in statistics—some advanced and complicated. In mathematics, they're technically defined as the dimension of the domain of a random vector.
Hamzah
But we won't get into that. Because degrees of freedom are generally not something you needto understand to perform a statistical analysis—unless you’re a research statistician, or someone studying statistical theory.
Hamzah
And yet, enquiring minds want to know. So for the adventurous and the curious, here are some examples that provide a basic gist of their meaning in statistics.
Hamzah
The Freedom to Vary First, forget about statistics. Imagine you’re a fun-loving person who loves to wear hats. You couldn't care less what a degree of freedom is. You believe that variety is the spice of life Unfortunately, you have constraints. You have only 7 hats. Yet you want to wear a different
Hamzah
hat every day of the week. On the first day, you can wear any of the 7 hats. On the second day, you can choose from the 6 remaining hats, on day 3 you can choose from 5 hats, and so on.
Hamzah
When day 6 rolls around, you still have a choice between 2 hats that you haven’t worn yet that week. But after you choose your hat for day 6, you have no choice for the hat that you wear on Day 7. You must wear the one remaining hat. You had 7-1 = 6 days of “hat” freedom—in which the hat you wore
Hamzah
That’s kind of the idea behind degrees of freedom in statistics. Degrees of freedom are often broadly defined as the number of "observations" (pieces of information) in the data that are free to vary when estimating statistical parameters.
Hamzah
please help me understand binomial distribution
Nnenna Reply
binomial distribution and poisson both are used to estimate the number of successes probable against the. probable failures. the difference is only that BINOMIAL dist. is for discrete data while POISSON is used for continuous data.
Salman
What do you need to understand?
Angela
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution
Hamzah
poisson distribution is also for discrete data set. The difference is when the probability of occurring an event is very little and the sample size is extra large then we use poisson distribution.
Neil
Neil yes you got it and very interested answer you gave
jamilu
How to know if the statement is 1 tail or 2 tail?
Coleen Reply
1 tail if greater than pr less than.2 tail if not equal.
Jojo
in such a case there is no sufficient information provided to develop an alternative hypothesis and we can decide between only two states i.e either the statement is EQUAL TO or NOT EQUAL TO under given conditions
Salman
for 1tail there must be certain criteria like the greater than or less than or some probability value that must be achieved to accept or reject the original hypothesis.
Salman
for example if we have null hypothesis Ho:u=25 Ha:u#25(not equal to 25) it would be two tail if we say Ho:u=25 Ha:u>or Ha:u<25 it would be consider as one tail I hope you will be understand #Coleen
Shabir
yes its true. now you have another problem. so share.
ibrar
what is z score
Esperanza Reply
How to find z score through calculator
Esperanza
Different data sets will have different means and standard deviations, so values from one set cannot always be compared directly with those from another. The z-score standardizes normally distributed data sets, allowing for a proper comparison and a consistent definition of percentiles across data s
Hamzah
what are random number
Saif Reply
how to compute the mean with a long method
Fria Reply
there is a shortcut method for calculating mean long methid doesn't make any sense.
Neil
what are probability
Saif
probability mass function
Saif
probability density function
Saif
there are many definitions of probability. which one is, the ratio of favourable outcomes & total outcomes.
suhail
distribution used for modeling/(find probabilities) of discrete r.v. is called p.m.f
suhail
distribution used for modeling/(find probabilities) of continued r.v, called p.d.f
suhail
lets use short method using calculator.... store yo data n smply get your mean
Flavian
if 1 calorie =4.12 kj, what is the total kj value of this dish
Jacqueline Reply
summation of values of x1 x2 x3 ,,,,xn divided by total number n if it is with frequency its like this summation of values of x1f1+x2f2+x3f3+xnfk divided by summation of frequencies like f1+f2+f3+fk
farah Reply
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QuizOver Reply

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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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