Using the normal distribution, there is a 0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean 
and standard deviation 
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
The probability that a randomly selected cyclist will take at least 2.45 hours to complete the race is <u>one subtracted by the p-value of Z when X = 2.45</u>, hence:
Z = -0.1
Z = -0.1 has a p-value of 0.4602.
1 - 0.4602 = 0.5398.
0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.
More can be learned about the normal distribution at brainly.com/question/4079902
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Alrighty, let's think of it like this: You are trying to fill a box with a bunch of sports balls. You have tiny little golf balls, and you have giant bowling balls. You need to fill this same box all the way up.
If you fill it with the tiny golf balls, you are going to need a <em>whole lot of them!</em>
If you are putting in bowling balls, only a few of them will fit, because they are so much bigger.
When it comes to your fraction, the box is the the number 8/10. That number will not change because we are not changing the size of the box.
We are just changing what we are filling it with. Manny, can fit 8 parts, or in this case balls, into the box.
It says Ana uses fewer parts, so she cannot fit as many in as Manny.
This means that Manny would have the golf balls, since he can fit more in than Ana, who must have the bowling balls.
So which is bigger? A bowling ball or a golf ball?
A bowling ball, which is what Ana has. So <u><em>Ana's part will be bigger</em></u> in size.
If 1 inch represents 20 miles, then 5 inches should represent <em>5 times as many miles</em>, or 20 x 5 = 100 miles.
This is completing the square.
So x^2-6x-12=0
Add 12 to both sides so x^2-6x=12
Now take half the x term and square it. Add this number to both sides.
So x^2-6x+9=12+9
Which is the same as (x-3)^2=21
This is answer 2.
