Answer:
So then we expect the 99.7% of the finishing times would be between 68.5 s and 83.5 s for the 400 meters race
Step-by-step explanation:
Let X the random variable who represent the finishing times.
From the problem we have the mean and the standard deviation for the random variable X.
So then the parameters are
On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:
The probability of obtain values within one deviation from the mean is 0.68, within two deviations we have 0.95 and within 3 deviations from the mean is 0.997
And from this rule we have 99.7 % of the values within 3 deviations from the mean, so we can find the limits like this:
So then we expect the 99.7% of the finishing times would be between 68.5 s and 83.5 s for the 400 meters race
The middle 99.7% of Tyler's finishing times in the 400 meter race is from 68.5 seconds to 83.5 seconds.
The empirical rule, also known as the 68-95-99.7 rule, states that for data that follows a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
To determine the interval of times that represents the middle 99.7% of Tyler's finishing times, we need to find the range of values that is three standard deviations above and below the mean.
Using the given mean of 76 seconds and standard deviation of 2.5 seconds, we can calculate the interval of times as follows:
Lower Limit: 76 - (3 * 2.5) = 76 - 7.5 = 68.5 seconds
Upper Limit: 76 + (3 * 2.5) = 76 + 7.5 = 83.5 seconds
Therefore, the interval of times that represents the middle 99.7% of Tyler's finishing times is from 68.5 seconds to 83.5 seconds.
Learn more about Empirical rule here:
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Which describes the meaning of f(x)?
a. A customer earns 1 free night per 10 nights stayed.
b. A customer starts with 1 free night and then earns another free night after every 10 nights stayed.
c.A customer earns x – 10 free nights for every 10 nights stayed.
d. A customer earns 10 free nights after x number of nights stayed.
Answer: option a. A customer earns 1 free night per 10 nights stayed.
Explanation:
Building a table can help you:
x: number of nigths stayed ---------- f(x) = 1/x: number of free nights
10 --------------------------------------------- 10/10 = 1
20 -------------------------------------------- 20/10 = 2
30 -------------------------------------------- 30/10 = 3
40 -------------------------------------------- 40/10 = 4
Then, the pattern permits you to conclude that a customer earns 1 free night per each 10 nights stayed, which is the option a.
Answer: a. A customer earns 1 free night per 10 nights stayed.
Step-by-step explanation:
A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.
When , we put x=1, we get
Here f(1) represents the number of free nights earned by customer is 1 per 10 nights stayed.
Hence, the a customer earns 1 free night per 10 nights stayed.
Answer:
6852 feet .
Step-by-step explanation:
Refer the attached figure
The chairlift at a ski resort rises a total of 2600 feet from where it starts. i.e.AB = 2600 feet
The angle of elevation is about 22.3 degrees.i.e.∠ACB= 22.3°
We are supposed to find How far do riders travel on the lift i.e.AC
In ΔABC
We will use trigonometric ratio
So, riders travel 6852 feet .
Answer:
First part is 1:2 because there is 1 hour to every 2 shows. Second part is 3:6 shows because 3 hours is 6 shows. Hope this helps, please rate brainiest answer!