Out of 2,000 random but normally distributed numbers with a mean of 45 and a standard deviation of x, approximately 1,360 numbers are found to be between 40 and 50. what is the value of x? a. 5 b. 10 c. -5 d. 680

A. 5

Step-by-step explanation:

It says that the sample is normally distributed, which means it follows the bell curve in terms of spreading.  That means that 68% of the numbers are within two standard deviations, centered on the mean, one standard deviation below, one up.

That's confirmed by the fact that 1,360 numbers (exactly 68% of 2,000) are between 40 and 50.  Since the mean is 45, that gives a spread of ± 1 standard deviation for 68% of the numbers.

One standard deviation goes from 40 to 45, another from 45 to 50.

So, the standard deviation of this sample is 5.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

she gotta workk that a 2

step-by-step explanation: