Bowie started painting at 9:40 a.m. and painted until 11:00. How long did he paint?

suppose X and Y are independent random variables, both with normal distributions. If X has a mean of 45 with a standard deviatio

djyliett [7]

Answer:

0.9772 = 97.72% probability that a randomly generated value of X is greater than a randomly generated value of Y

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

$\mu_X = 45, \sigma_X = 4, \mu_Y = 35, \sigma_Y = 3$

What is the probability that a randomly generated value of X is greater than a randomly generated value of Y

This means that the subtraction of X by Y has to be positive.

When we subtract two normal variables, the mean is the subtraction of their means, and the standard deviation is the square root of the sum of their variances. So

$\mu = \mu_X - \mu_Y = 45 - 35 = 0$

$\sigma = \sqrt{\sigma_X^2+\sigma_Y^2} = \sqrt{25} = 5$

We want to find P(X > 0), that is, 1 subtracted by the pvalue of Z when X = 0. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0 - 10}{5}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228

1 - 0.0228 = 0.9772

0.9772 = 97.72% probability that a randomly generated value of X is greater than a randomly generated value of Y

4 0

3 years ago

What is an equation of the line that passes through the point (-5,3)(−5,3) and is parallel to the line 3x-5y=303x−5y=30?

rosijanka [135]

The equation of the line which passes through the point (-5, 3) and is parallel to the equation 3x -5y = 30 is; 3x -5y = 30.

<h3>What is the equation of the line?</h3>

Since the line is parallel to the given line; 3x -5y = 30 whose slope is; 3/5.

Hence, since the two lines have equal slopes;

3/5 = (y-3)/(x-(-5))

3/5 = (y-3)/(x+5)

5y -15 = 3x +15

3x -5y = 30

Read more on equation of a line;

brainly.com/question/1461621

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3 0

1 year ago

How do i do #3? I dont know how to do the whole problem.

lisov135 [29]

You have to put the problem down we cant help you if its not there
sorry but please put equation in or problem

3 0

3 years ago

The arithmetic mean (average) of four numbers is 85. If the largest of these numbers is 97, find the mean of the remaining three

ser-zykov [4K]

Answer: 81

Step-by-step explanation:

Mean of four nos = 85

Score = 85 x 4 = 340

Deduct 97 from 340 = 243

Mean of three nos. 243/3 = 81

3 0

3 years ago

Using the given information, find the following parameters.

Oksi-84 [34.3K]

Answer:

1. Mode = 2.60

2. Mean = 3.71

3. Median = 3.12

Step-by-step explanation:

1.

The mode, in statistics, is the number that occurs the "most". If there is no number occurring more than others, there is no mode. Also, there can be more than 1 mode as well.

We need to arrange the number from least to greatest for our ease. Let's do this first.

2.16, 2.19, 2.53, 2.60, 2.60, 2.94, 3.30, 3.67, 4.65, 5.40, 5.76, 6.71

Is there any number occurring more than once?

Yes, that's 2.60, so that's the mode.

Mode = 2.60

2.

The mean is the average. We take the sum of all the numbers and divide by the number of numbers [there are 12 numbers].

We have to round the answer to nearest hundredth (2 decimal places).

Let's calculate the sum.

SUM(2.16, 2.19, 2.53, 2.60, 2.60, 2.94, 3.30, 3.67, 4.65, 5.40, 5.76, 6.71) = 44.51

Now, the mean:

Mean = 44.51/12 = 3.71

3.

Median is the "middle" number when the numbers are arranged from least to greatest. If there are a set of even numbers, n = even, then we divide n by 2 and take the average of that number and next number.

Here n = 12

so 12/2 = 6

So we take average of 6th and 7th number to get the median.

First, let's find 6th and 7th number from the list.

6th number = 2.94

7th number = 3.30

We take average of that to find Median.

Median = (2.94+3.30)/2 = 3.12

6 0

3 years ago