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
To find the probability of getting at most 4 tails when a coin is tossed 5 times, you can use the formula for a binomial distribution. The probability of getting k successes in n trials, where the probability of success is p, is given by:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
In this case, the coin tosses are independent and there is a 1/2 probability of getting tails (success) on each toss. So, to find the probability of at most 4 tails, we need to find the probability of:
P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
Calculating each term using the formula above, we get:
P(X = 0) = (5 choose 0) * (1/2)^0 * (1-1/2)^(5-0) = 1 * 1 * (1/2)^5 = 1 * 1 * 1/32 = 1/32
P(X = 1) = (5 choose 1) * (1/2)^1 * (1-1/2)^(5-1) = 5 * 1/2 * 1/2^4 = 5/32
P(X = 2) = (5 choose 2) * (1/2)^2 * (1-1/2)^(5-2) = 10 * 1/4 * 1/2^3 = 10/32
P(X = 3) = (5 choose 3) * (1/2)^3 * (1-1/2)^(5-3) = 10 * 1/8 * 1/2^2 = 10/64
P(X = 4) = (5 choose 4) * (1/2)^4 * (1-1/2)^(5-4) = 5 * 1/16 * 1/2^1 = 5/32
Adding these probabilities together, we get:
P(at most 4 tails) = 1/32 + 5/32 + 10/32 + 10/64 + 5/32 = 31/32
Therefore, the answer is option D) 31/32.
Moving on to the second question, we need to find the number of different arrangements of the letters in the word "doodle".
To do this, we first need to determine the number of total possibilities if all the letters are unique. In this case, we have 6 letters, so there are 6 possibilities for the first letter, 5 for the second, 4 for the third, and so on. This gives us 6 * 5 * 4 * 3 * 2 * 1 = 720 possibilities.
However, since the letter "o" appears twice, we need to account for the fact that swapping the two "o"s does not result in a different arrangement. So, we divide the total number of possibilities by 2 to remove the duplicates.
Therefore, the number of different arrangements of the letters in the word "doodle" is 720 / 2 = 360.
So, the correct answer is option A) 180.