Suppose a normally distributed set of data with 7800 observations has a mean of 188 and a standard deviation of 18. Use the 68-95-99.7 Rule to determine the number of observations in the data set expected to be below a value of 242. Round your result to the nearest single observation.

7788 observations are expected to be below a value of 242.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 188, standard deviation = 18

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

Percentage of observations below 242:

242 = 188 + 3*18

So 242 is three standard deviations above the mean

Of the measures below the mean, all are below 242.

Of the measures above the mean, 99.7% are between the mean of 188 and three standard deviations above the mean(242). So the percentage is:

[tex}P = 0.5 + 0.997*0.5 = 0.9985[/tex]

Number of observations below 242:

99.85% of 7800 observations

0.9985*7800 = 7788

7788 observations are expected to be below a value of 242.

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'.

mean, 40.6

step-by-step explanation: