The number of golf balls ordered by customers of a pro shop has the following probability distribution. Find the mean.
x|P(x)
3|0.14
6|0.05
9|0.36
12|0.35
15|0.10
A. 7.86
B. 9
C. 6.99
D. 9.66
I did:
3(.14) + 6(.05) + 9(.36) + 12(.35) + 15(.1)
and got 9.66
How did you get 6.99 ??
Alright, let's calculate the mean of this distribution.
To find the mean, we need to multiply each value of x by its corresponding probability, then sum up all these products. So, let's do some math gymnastics together!
(3 * 0.14) + (6 * 0.05) + (9 * 0.36) + (12 * 0.35) + (15 * 0.10) = ?
First, we multiply each value of x by its corresponding probability:
0.42 + 0.30 + 3.24 + 4.20 + 1.50 = ?
Now, we sum up the products:
0.42 + 0.30 + 3.24 + 4.20 + 1.50 = 9.66
So, the mean number of golf balls ordered is 9.66.
Therefore, the answer is option D. 9.66.
Remember, it's always best to have extra golf balls handy in case you accidentally hit a squirrel and need a spare!
To find the mean of a probability distribution, you need to multiply each possible value by its corresponding probability, and then sum up all these products. The mean, also known as the expected value, can be calculated using the formula:
Mean = Σ(x * P(x))
where x represents the possible values and P(x) represents the corresponding probabilities.
Let's calculate the mean together:
Mean = (3 * 0.14) + (6 * 0.05) + (9 * 0.36) + (12 * 0.35) + (15 * 0.10)
Mean = 0.42 + 0.30 + 3.24 + 4.2 + 1.5
Mean = 9.66
Therefore, the mean number of golf balls ordered is 9.66.
So the correct answer is D. 9.66.