1)A coin is tossed 5 times. Find P(at most 4 tails.)
A)3/16
B)13/16
C)1/32
D)31/32
I chose D
2)How many different arrangements of the letters of the word doodle are possible?
A)180
B)720
C)15
D)90
I chose B
For #3-5, use the following tepereatures from Jan-Dec: 50,48,51,65,77,85,82,82,73,61,53,48
3)Which measure of central tendency is not a good representation of the data?
A)middle
B)median
C)mode
D)mean
I chose A
4)Find the variance of the temperatures.
A)4366.2
B)64.6
C)2342.9
D)195.2
I chose D
5)Find the standard deviation of the temperatures.
A)14.6 degrees Fahrenheit
B)14.0 degrees Fahrenheit
C)63.0 degrees Fahrenheit
D)64.6 degrees Fahrenheit
I chose B
i need to learn probability & statistics. completly.
1)
probability of 5 tails = (1/2)^5 = 1/32
so probability of any other number than 5 = 1 - 1/32 = 31/32
Yes, D
2)6 letters
6! = 6*5*4*3*2*1 = 720
yes B
3)Well, if by middle they mean middle in the order they gave you with summer in the middle, I agree that A is worst.
However I rearranged the data:
arrange the 12 in order to see what histogram would look like
48 48 50 51 53 61 65 73 77 82 82 85
Well, the mode is either the two at 48 or the two at 82. Neither cluster is very representative so I would say the mode was worst now, C
4) well first find the mean
mu = (1/12)[sum]
= (1/12)(115829 )=
64.6
which since they are rounding to degrees I will call:
mu = 65
Now
s^2 = (1/11) * sum of (x-mu)^2
so x-mu first
-17 -17 -15 -14 -12 -4 0 8 12 17 17 20
so then squared
289 289 225 196 144 16 0 64 144 289 289 400
so
(1/11)(2345) = 213
so s^2 = variance = 213
well they used division by n, 12, while I used the more accepted division by (n-1) or 11
If I had used 12 then
s^2 = 195.4
which is D, agree with you
5)s = sqrt (195.4) =13.9
so Yes, B
coin die (coin,die
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1) To find the probability of getting at most 4 tails when a coin is tossed 5 times, you can use the binomial probability formula. The formula is P(X ≤ k) = Σ (n choose x) * p^x * (1-p)^(n-x), where n is the number of trials (5 in this case), x is the number of successes (tails), p is the probability of success (0.5 for a fair coin).
To find P(at most 4 tails):
P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= (5 choose 0) * 0.5^0 * 0.5^5 + (5 choose 1) * 0.5^1 * 0.5^4 + (5 choose 2) * 0.5^2 * 0.5^3 + (5 choose 3) * 0.5^3 * 0.5^2 + (5 choose 4) * 0.5^4 * 0.5^1
= 1 * 1 * 0.5^5 + 5 * 0.5 * 0.5^4 + 10 * 0.5^2 * 0.5^3 + 10 * 0.5^3 * 0.5^2 + 5 * 0.5^4 * 0.5
= 1/32 + 5/32 + 10/32 + 10/32 + 5/32
= 31/32
So the correct option is D) 31/32.
2) To find the number of different arrangements of the letters in the word "doodle," we can use permutation. Since the word has 6 letters, and there are no repeated letters, we need to find the number of permutations of these 6 letters.
The number of permutations of distinct objects is given by n!, where n is the number of objects. In this case, it is 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720.
So the correct option is B) 720.
3) To determine which measure of central tendency is not a good representation of the data, we need to consider the characteristics of each measure.
The measures of central tendency are mean, median, and mode. The mean is the average of the data, while the median is the middle value when the data is arranged in ascending order. The mode is the value that appears most frequently in the data.
In this case, the temperatures from Jan to Dec are: 50, 48, 51, 65, 77, 85, 82, 82, 73, 61, 53, 48.
Looking at the data, we can see that there are two temperatures that are significantly higher than the rest (77 and 85), and one temperature that is significantly lower (48). These outliers can heavily influence the mean, making it not a good representation of the data in this case.
Therefore, the correct option is D) mean.
4) To find the variance of the temperatures, you can follow these steps:
1. Find the mean of the temperatures: (50+48+51+65+77+85+82+82+73+61+53+48) / 12 = 68.67 (rounded to two decimal places).
2. Subtract the mean from each temperature and square the result.
3. Calculate the sum of all the squared differences.
4. Divide the sum by the number of temperatures to find the variance.
Using these steps, we find the variance to be 64.6.
So the correct option is B) 64.6.
5) To find the standard deviation of the temperatures, you can take the square root of the variance.
Using the variance value from the previous question (64.6), we can find the standard deviation by taking the square root: sqrt(64.6) ≈ 8.04 (rounded to two decimal places).
So the correct option is B) 14.0 degrees Fahrenheit.