Hello please please respond. I know it’s late but I need help with my math homework as soon as possible please I’m so desperate

Question

Question 1: Identify the variance and the standard deviation of the given data set.

{7, 8, 6, 3, 4, 12, 14, 10}

 

A.) variance: 12.75

standard deviation: 12.75

 

B.) variance: 7.2

standard deviation: 3.57

 

C.) variance: 12.75

standard deviation: 3.57

 

D.) variance: 12.75

standard deviation: 7.2

 

  

 

Question 2: The probability distribution of the number of cars passing through an intersection each day based on past data is given below. Identify the expected number of cars passing through the intersection for one day.

 

A.)121

B.) 125

C.) 126

D.) 123

 

Answer 1

C.) mean (xbar) is 8.

use formula: variance = sum (x(i) - xbar)^2/n

and standard deviation is square root of variance

where n = 8.

variance: 12.75

standard deviation: 3.57

expected value = sum of (x * P(x)) for x = 1 to 4:

152 * 0.35 + 89 * 0.15 + 94 * 0.26 + 146 * 0.24 = 126.03 ~ 126 (c)