STAT 100 Midterm: STAT100 ALL-SECTIONS FALL1996 0000 MID EXAM

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turquoisegnu128

15 Feb 2019

School

University of Maryland

Department

Statistics and Probability

Course

STAT 100

Professor

All

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Document Summary

You may use calculators, but not books or notes. Do not spend too much time on any one problem. Nal answer to a question: given is the following sample data: 5, 5, 5, 2, 3. Calculate the sample mean, sample standard deviation, and median. (b) (5 pts. ) Draw a histogram, with bin (interval) length one. 2(a) suppose x is a random variable with mean 2 and with standard deviation 3. What are the mean and standard deviation of the random variable. Y ? (no explanation required. ) (b) two fair dice are rolled. What is the probability that the sum of the numbers rolled is 5: suppose a, b and c are three events such that b and c are mutually exclusive, A and b are independent, p(a)=. 6 , p(b)=. 3 and p(cb)=. 25 .

Related Questions

You are interested in how much time students spend on the internet each day. Here are data on the time spent on the internet (in minutes) for a particular day reported by a random sample of 30 students at a large college:

a) Make a histogram of these data. Is the shape symmetric or skewed?

b) Find the 5 number summary and P_65.

c) Find the mean and sample standard deviation.

d) Are there any outliers? Justify your answer.

e) Would it be better to use the mean and standard deviation or the median and IQR to describe the centre and spread of this distribution? why?

ceruleanhedgehog638

The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season

x	P(x)
0	0.167
1	0.3289
2	0.2801
3	0.149
4	0.0382
5	0.0368

The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated?

a.Compute the theoretical mean of the random variable X for the given probability distribution.

Meu = ?

b. Compute the theoretical standard deviation of the random variable X for the given probability distribution.

Sigma =?

c.Approximate the mean of the random variable X based on the simulation for 25 games.

Xbar=?

d. Approximate the standard deviation of the random variable X based on the simulation for 25 games.

S=?

The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season x P(x) 0 0.167 1 0.3289 2 0.2801 3 0.149 4 0.0382 5 0.0368 The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated? a.Compute the theoretical mean of the random variable X for the given probability distribution. Meu = ? b. Compute the theoretical standard deviation of the random variable X for the given probability distribution. Sigma =? c.Approximate the mean of the random variable X based on the simulation for 25 games. Xbar=? d. Approximate the standard deviation of the random variable X based on the simulation for 25 games. S=?

oliverabbit290

Rules of dice game:

• All players start with 10 points

• A dice is rolled, and if the number on the dice is 1, 2, 3, 4 or 5, this number is added to each player's score. If the number is 6, the score off all players is reduced to zero

• Before the dice is rolled each player is given the choice of continuing or taking their current score as their final score.

• This process is repeated until a 6 is rolled and the game ends. All players still playing at this point receive zero as their final score.

Suppose that you choose to play the first dice roll.

(i) Compute the expected value and standard deviation of your score after the first dice roll.

(ii) On average, do you do worse or better than someone who choose not to play and take 10 as their final score?

Now suppose that a 6 was not rolled and you chooses to continue playing

(iii) On average, what score would you have before the dice is rolled?

(iv) Compute the expected value for your score after the second dice roll.

(v) On average, do you do worse or better than someone who choose to stop playing after 1 dice roll?

(vi) Is there an optimal number of dice rolls you should continue playing for? Explain your reasoning.

(vii) If the rules are changed such that when the number is 2, 3, 4, 5 or 6, this number is added to your score. While if the number is 1, your score is reduced to zero. Discuss how this affects the optimal number of dice rolls you should continue playing for.

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STAT 100 Midterm: STAT100 ALL-SECTIONS FALL1996 0000 MID EXAM

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