The letter "t" makes up an estimated 10% of a certain language. Assume this is still correct. A random sample of 500 letters i
s taken from a randomly selected, large book and the t's are counted. Find the approximate probability that the random sample of 500 letters will contain 9.1% or fewer t's.
1 answer:
Answer:
0.2755
Step-by-step explanation:
We intend to make use of the normal approximation to the binomial distribution.
First we'll check to see if that approximation is applicable.
For p=10% and sample size n = 500, we have ...
pn = 0.10(500) = 50
This value is greater than 5, so the approximation is valid.
__
The mean of the distribution we'll use as a model is ...
µ = p·n = 0.10(500)
µ = 50
The standard deviation for our model is ...
σ = √((1-p)µ) = √(0.9·50) = √45
σ ≈ 6.708204
__
A continuity correction can be applied to better approximate the binomial distribution. We want p(t ≤ 9.1%) = p(t ≤ 45.5). For our lookup, we will add 0.5 to this limit, and find p(t ≤ 46).
The attached calculator shows the probability of fewer than 45.5 t's in the sample is about 0.2755.
You might be interested in
Answer:
Question 4:
Question 5:
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: where <em>m</em> is the slope of the line and <em>b</em> is the y-intercept (the y-coordinate of the point where the line crosses the y-axis).
<u>Question 4</u>
<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>
where two points that pass through the line are
and
In the graph, two easy-to-identify points on the line are (-5,4) and (5,-4). Plug these into the equation:
Therefore, the slope of the line is . Plug this into
as the slope (<em>m</em>):
<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>
On the graph, we can see that the line crosses the y-axis when y is 0. Therefore, the y-intercept (<em>b</em>) is 0. Plug this into :
<u>Question 5</u>
<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>
Two easy-to-identify points are (-1,2) and (0,-3). Plug these into the equation:
Therefore, the slope is -5. Plug this into :
<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>
On the graph, we can see that the line crosses the y-axis at the point (0,-3). The y-coordinate of this point is -3. Therefore, the y-intercept (<em>b</em>) is -3. Plug this into :
I hope this helps!