This question has two parts, First, answer Part A Then, answer Part B
1 answer:
You might be interested in
Answer:
Here ya go ! :)
Step-by-step explanation:
Step-by-step explanation:
Given that,
- Length of the one portion of the board = x feet
- Length of the another portion = (7x – 9) feet
According to the question,
Total length = Sum of the length of the two pieces
Total length = {x + (7x – 9)} feet
Total length = {x + 7x – 9} feet
<u>Total length = (8x – 9) feet</u>
Therefore, the total length of the board as a simplified expression in x is (8x – 9) feet.
Answer:
(a) The histogram is shown below.
(b) E (X) = 4.2
(c) SD (X) = 2.73
Step-by-step explanation:
Let <em>X</em> = <em>r</em><em> </em>= a driver will tailgate the car in front of him before passing.
The probability that a driver will tailgate the car in front of him before passing is, P (X) = <em>p</em> = 0.35.
The sample selected is of size <em>n</em> = 12.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 12 and <em>p</em> = 0.35.
The probability function of a binomial random variable is:
(a)
For <em>X</em> = 0 the probability is:
For <em>X</em> = 1 the probability is:
For <em>X</em> = 2 the probability is:
Similarly the remaining probabilities will be computed.
The probability distribution table is shown below.
The histogram is also shown below.
(b)
The expected value of a Binomial distribution is:
The expected number of vehicles out of 12 that will tailgate is:
Thus, the expected number of vehicles out of 12 that will tailgate is 4.2.
(c)
The standard deviation of a Binomial distribution is:
The standard deviation of vehicles out of 12 that will tailgate is:
Thus, the standard deviation of vehicles out of 12 that will tailgate is 2.73.
