# 0.2 Practice tests (1-4) and final exams  (Page 16/36)

 Page 16 / 36

83 . $\Sigma X\sim N\left(n{\mu }_{x},\left(\sqrt{n}\right)\left({\sigma }_{x}\right)\right)$ so $\Sigma X\sim N\left(4000,28.3\right)$

84 .The probability is 0.50, because 5,000 is the mean of the sampling distribution of sums of size 40 from this population. Sums of random variables computed from a sample of sufficient size are normally distributed, and in a normal distribution, half the values lie below the mean.

85 . Using the empirical rule, you would expect 95 percent of the values to be within two standard deviations of the mean. Using the formula for the standard deviation is for a sample sum: $\left(\sqrt{n}\right)\left({\sigma }_{x}\right)=\left(\sqrt{40}\right)\left(7\right)=44.3$ so you would expect 95 percent of the values to be between 5,000 + (2)(44.3) and 5,000 – (2)(44.3), or between 4,911.4 and 588.6.

86 . $\mu -\left(\sqrt{n}\right)\left({\sigma }_{x}\right)=5000-\left(\sqrt{40}\right)\left(7\right)=4955.7$

87 . $5000+\left(2.2\right)\left(\sqrt{40}\right)\left(7\right)=5097.4$

## 7.3: using the central limit theorem

88 . The law of large numbers says that as sample size increases, the sample mean tends to get nearer and nearer to the population mean.

89 . You would expect the mean from a sample of size 100 to be nearer to the population mean, because the law of large numbers says that as sample size increases, the sample mean tends to approach the population mea.

90 . X ~ N (0.10, 0.20)

91 . $\overline{X}\sim N\left({\mu }_{x},\frac{{\sigma }_{x}}{\sqrt{n}}\right)$ and the standard deviation of a uniform distribution is $\frac{b-a}{\sqrt{12}}$ . In this example, the standard deviation of the distribution is $\frac{b-a}{\sqrt{12}}=\frac{0.10}{\sqrt{12}}=0.03$
so $\overline{X}\sim N\left(0.15,0.003\right)$

92 .

## 8.1: confidence interval, single population mean, population standard deviation known, normal

Use the following information to answer the next seven exercises. You draw a sample of size 30 from a normally distributed population with a standard deviation of four.

1 . What is the standard error of the sample mean in this scenario, rounded to two decimal places?

2 . What is the distribution of the sample mean?

3 . If you want to construct a two-sided 95% confidence interval, how much probability will be in each tail of the distribution?

4 . What is the appropriate z -score and error bound or margin of error ( EBM ) for a 95% confidence interval for this data?

5 . Rounding to two decimal places, what is the 95% confidence interval if the sample mean is 41?

6 . What is the 90% confidence interval if the sample mean is 41? Round to two decimal places

7 . Suppose the sample size in this study had been 50, rather than 30. What would the 95% confidence interval be if the sample mean is 41? Round your answer to two decimal places.

8 . For any given data set and sampling situation, which would you expect to be wider: a 95% confidence interval or a 99% confidence interval?

## 8.2: confidence interval, single population mean, standard deviation unknown, student’s t

9 . Comparing graphs of the standard normal distribution ( z -distribution) and a t -distribution with 15 degrees of freedom ( df ), how do they differ?

10 . Comparing graphs of the standard normal distribution ( z -distribution) and a t -distribution with 15 degrees of freedom ( df ), how are they similar?

Use the following information to answer the next five exercises. Body temperature is known to be distributed normally among healthy adults. Because you do not know the population standard deviation, you use the t-distribution to study body temperature. You collect data from a random sample of 20 healthy adults and find that your sample temperatures have a mean of 98.4 and a sample standard deviation of 0.3 (both in degrees Fahrenheit).

#### Questions & Answers

If a random variable X takes only two values -2 and 1 such that 2 P[X=- 2]=P[X=1]=P, then find variance of x.
Dikshita Reply
2.5
Anirban
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
hi friends am new here, hope am welcome
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
dev OS
Virendra
searching for motivation to learn stat
Nija
purpose of of statistics
mukesh
ya..
mukesh
tamil people yaraavathu inrukkingala
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

### Read also:

#### Get the best Introductory statistics course in your pocket!

Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

 By By By Brooke Delaney By Hope Percle By OpenStax By By Richley Crapo By Angelica Lito By OpenStax By By Jill Zerressen By Anindyo Mukhopadhyay