Download FAMAT 2012 State Convention Statistics Bowl #1 In a box, 6

FAMAT 2012 State Convention
Statistics Bowl #1
In a box, 6 oranges weigh 2, 2, 3, 3, 4, and 4 oz. In another box, 6 apples weigh 2,
3, 3, 4, 5, and 5 oz. The fruits from the two boxes are combined into one box. If a
fruit from this new box is chosen at random, calculate the probability that a fruit is
more than 3 ounces.
FAMAT 2012 State Convention
Statistics Bowl #1
In a box, 6 oranges weigh 2, 2, 3, 3, 4, and 4 oz. In another box, 6 apples weigh 2,
3, 3, 4, 5, and 5 oz. The fruits from the two boxes are combined into one box. If a
fruit from this new box is chosen at random, calculate the probability that a fruit is
more than 3 ounces.
FAMAT 2012 State Convention
Statistics Bowl #2
In tennis, the first person to win six games wins the match. When playing Bishoy,
the probability that Dhyan wins any given game of a tennis match is .9.
Let A=the probability that Dhyan wins the match in exactly six games. Round to
two decimals.
Let B=the probability that Dhyan wins the match in at most nine games. Round to
two decimals.
Find A+B
FAMAT 2012 State Convention
Statistics Bowl #2
In tennis, the first person to win six games wins the match. When playing Bishoy,
the probability that Dhyan wins any given game of a tennis match is .9.
Let A=the probability that Dhyan wins the match in exactly six games. Round to
two decimals.
Let B=the probability that Dhyan wins the match in at most nine games. Round to
two decimals.
Find A+B
FAMAT 2012 State Convention
Statistics Bowl #3
The scores for Mr. Fraser’s calculus test have a mean of 75 and a standard deviation of 4. He
wants to create a linear transformation of these scores so that they have a mean of 84 and a
standard deviation of 5. Eric scores an 83 before the curve. Jarrod scores a 98 after the curve.
Let A=slope of the linear transformation equation
Let B= y-intercept of the linear transformation equation
Let C= Eric’s new score
Let D=Jarrod’s original score
Find A+B+C+D
FAMAT 2012 State Convention
Statistics Bowl #3
The scores for Mr. Fraser’s calculus test have a mean of 75 and a standard deviation of 4. He
wants to create a linear transformation of these scores so that they have a mean of 84 and a
standard deviation of 5. Eric scores an 83 before the curve. Jarrod scores a 98 after the curve.
Let A=slope of the linear transformation equation
Let B= y-intercept of the linear transformation equation
Let C= Eric’s new score
Let D=Jarrod’s original score
Find A+B+C+D
FAMAT 2012 State Convention
Statistics Bowl #4
A three digit number is made from randomly choosing digits from 0 through 9
inclusive. Each digit is used only once (that is, if a digit is chosen, it cannot be
chosen again).
Let A= the probability that the number is divisible by 5
Let B= the probability that the number is divisible by 2
Find A/B
FAMAT 2012 State Convention
Statistics Bowl #4
A three digit number is made from randomly choosing digits from 0 through 9
inclusive. Each digit is used only once (that is, if a digit is chosen, it cannot be
chosen again).
Let A= the probability that the number is divisible by 5
Let B= the probability that the number is divisible by 2
Find A/B
FAMAT 2012 State Convention
Statistics Bowl #5
UC Berkeley has a large number of Asian students. The grades in English class of a random
sample of 100 Asian students are measured and the following results are obtained:
∑x =7800, ∑(x- )2=693
Let A = an unbiased estimate of the mean, µ, of the grades of these students
Let B = an unbiased estimate of the variance, σ2, of the grades of these students
Let C = the range of a 95% confidence interval to two decimal places
Find A+B+C
FAMAT 2012 State Convention
Statistics Bowl #5
UC Berkeley has a large number of Asian students. The grades in English class of a random
sample of 100 Asian students are measured and the following results are obtained:
∑x =7800, ∑(x- )2=693
Let A = an unbiased estimate of the mean, µ, of the grades of these students
Let B = an unbiased estimate of the variance, σ2, of the grades of these students
Let C = the range of a 95% confidence interval to two decimal places
Find A+B+C
FAMAT 2012 State Convention
Statistics Bowl #6
The weight of American men is normally distributed with a mean of 160 pounds
and standard deviation of 1.5 pounds.
Let A= proportion of American men that weigh 158-162 pounds (round to 4
decimal places)
Let B= proportion of American men that weigh less than 158 or greater than 162
pounds (round to 4 decimals)
Let C= the weight needed to be in the upper 20% of male weights (round to nearest
whole number)
Find A+B+C
FAMAT 2012 State Convention
Statistics Bowl #6
The weight of American men is normally distributed with a mean of 160 pounds
and standard deviation of 1.5 pounds.
Let A= proportion of American men that weigh 158-162 pounds (round to 4
decimal places)
Let B= proportion of American men that weigh less than 158 or greater than 162
pounds (round to 4 decimals)
Let C= the weight needed to be in the upper 20% of male weights (round to nearest
whole number)
Find A+B+C
FAMAT 2012 State Convention
Statistics Bowl #7
Muhammed and Abraham are brothers. Abraham always drives to school while Muhammed always runs
to school. The times taken to travel to school may be assumed to be independent and normally distributed.
The mean and the standard deviation for these times are shown in the table below.
Abraham driving
Muhammed running
Mean(min)
12
30
Standard Deviation (min)
2
3
Let A=probability that on any given day Muhammed takes more than 35 minutes to run to school
(round to three decimal places)
If Abraham drives to school five mornings in a row,
Let B=probability that the total time taken is less than 70 minutes. (round to three decimal places)
Let C=probability that on a particular day, the time taken by Muhammed to walk to school is
more than twice the time taken by Abraham to drive to school. (round to three decimal places)
Find A+B+C
FAMAT 2012 State Convention
Statistics Bowl #7
Muhammed and Abraham are brothers. Abraham always drives to school while Muhammed always runs
to school. The times taken to travel to school may be assumed to be independent and normally distributed.
The mean and the standard deviation for these times are shown in the table below.
Abraham driving
Muhammed running
Mean(min)
12
30
Standard Deviation (min)
2
3
Let A=probability that on any given day Muhammed takes more than 35 minutes to run to school
(round to three decimal places)
If Abraham drives to school five mornings in a row,
Let B=probability that the total time taken is less than 70 minutes. (round to three decimal places)
Let C=probability that on a particular day, the time taken by Muhammed to walk to school is
more than twice the time taken by Abraham to drive to school. (round to three decimal places)
Find A+B+C
FAMAT 2012 State Convention
Statistics Bowl #8
I toss a fair coin until I get five heads or five tails, whichever comes first. Let the
random variable X be the number of times I toss the coin.
Let A = the probability that X=9
Let B = the probability that X=5
Find A+B
FAMAT 2012 State Convention
Statistics Bowl #8
I toss a fair coin until I get five heads or five tails, whichever comes first. Let the
random variable X be the number of times I toss the coin.
Let A = the probability that X=9
Let B = the probability that X=5
Find A+B
FAMAT 2012 State Convention
Statistics Bowl #9
In a high school, the mean number of kids who fail math is 51. The teachers decide to use a new method
of teaching to lower the number of kids who do fail math. The results of the new method are as follows:
Class
# of kids who
fail
A
33
B
21
C
55
D
26
E
40
Carry out an appropriate test at the 10% significance level and find that p-value to 3 significant figures.
FAMAT 2012 State Convention
Statistics Bowl #9
In a high school, the mean number of kids who fail math is 51. The teachers decide to use a new method
of teaching to lower the number of kids who do fail math. The results of the new method are as follows:
Class
# of kids who
fail
A
33
B
21
C
55
D
26
E
40
Carry out an appropriate test at the 10% significance level and find that p-value to 3 significant figures.
FAMAT 2012 State Convention
Statistics Bowl #10
Eli loves a special bag of marbles. The marbles are supposed to be 30% brown, 20% white, 15%
yellow, 20% blue, 5% green, and 10% orange. But lately, Eli believes that these values are false.
Eli takes a random sample of 200 marbles and finds that there are 64 brown, 36 white, 30 yellow,
25 blue, 15 green, and 30 orange. Eli takes a chi-square test to test his hypothesis.
Let A = Chi-square value rounded to 3 decimal places
Let B = P-value rounded to 3 decimal places
Let C = Number of Degrees of Freedom
Find A+B+C
FAMAT 2012 State Convention
Statistics Bowl #10
Eli loves a special bag of marbles. The marbles are supposed to be 30% brown, 20% white, 15%
yellow, 20% blue, 5% green, and 10% orange. But lately, Eli believes that these values are false.
Eli takes a random sample of 200 marbles and finds that there are 64 brown, 36 white, 30 yellow,
25 blue, 15 green, and 30 orange. Eli takes a chi-square test to test his hypothesis.
Let A = Chi-square value rounded to 3 decimal places
Let B = P-value rounded to 3 decimal places
Let C = Number of Degrees of Freedom
Find A+B+C
FAMAT 2012 State Convention
Statistics Bowl #11
10 of Jarrod’s 15 test scores are 80, 83, 84, 93, 82, 78, 98, 97, 99, 88.
Let A= the mean
Let B= the first quartile
Let C= the third quartile
Let D= the sample variance
Find A+B+C+D
FAMAT 2012 State Convention
10 of Jarrod’s 15 test scores are 80, 83, 84, 93, 82, 78, 98, 97, 99, 88.
Let A= the mean
Let B= the first quartile
Let C= the third quartile
Let D= the sample variance
Find A+B+C+D
Statistics Bowl #11
FAMAT 2012 State Convention
Statistics Bowl #12
There are p people sitting around a circle. Each person votes for the person on their
right or their left randomly. The winner is the person with the most votes. If there
is a tie, the probability of winning is 1/n where n is the number of people tied. If
you vote for the person on your left, what is the probability that you win?
FAMAT 2012 State Convention
Statistics Bowl #12
There are p people sitting around a circle. Each person votes for the person on their
right or their left randomly. The winner is the person with the most votes. If there
is a tie, the probability of winning is 1/n where n is the number of people tied. If
you vote for the person on your left, what is the probability that you win?
FAMAT 2012 State Convention
Statistics Bowl #13
Given a regular deck of cards (52 cards, 12 face cards, 40 non-face cards)
how many different ways are there to deal one face card followed by a
non-face card?
FAMAT 2012 State Convention
Statistics Bowl #13
Given a regular deck of cards (52 cards, 12 face cards, 40 non-face cards)
how many different ways are there to deal one face card followed by a
non-face card?
FAMAT 2012 State Convention
Statistics Bowl #14
The cooling in a high school is to be increased on the third heated day during the
term. The probability that a day will be heated is 0.09.
Let A= the probability that the cooling is increased on the 25th day of the term
(round to 3 decimal places)
Let B= the day which heating is most likely to be increased
Find A+B
FAMAT 2012 State Convention
Statistics Bowl #14
The cooling in a high school is to be increased on the third heated day during the
term. The probability that a day will be heated is 0.09.
Let A= the probability that the cooling is increased on the 25th day of the term
(round to 3 decimal places)
Let B= the day which heating is most likely to be increased
Find A+B