6. Number of passengers who arrive at the platform in an Amtrack train station for the 2 pm train on a Saturday is a random variable with a mean of 180 and a standard deviation of 20. a) With what probability can we assert that there will be between 120 and 240 passengers

99.7%

Step-by-step explanation:

Mean number of passengers (μ) = 180 passengers

Standard deviation (σ) = 20 passengers

The number of standard deviation from the mean for the lower and upper bounds of the 120 to 240 passengers intervals are:

Therefore, all of the data is within 3 standard deviations from the mean. According to the empirical rule, 99.7% of the data is within 3 standard deviations from the mean. Therefore, we can assert with a 99.7% probability  that there will be between 120 and 240 passengers.

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.