I need so much help with this question from my Algebra homework very quickly please I am 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

Question 1: The variance of a data set is ∑ (X_i - mean)² / N where X_i = each individual data point, N = total number of data points. So, you subtract the mean from each data point, square that result, and add all differences, and finally divide by N. The standard deviation is the square root of the variance.

This can also be done on a scientific calculator.

answer: C

Question 2: Expected value for a day is found by multiplying each number of cars by the probability and summing all the results. 152 x 0.35 + 89 x 0.15 + 94 x 0.26 + 146 x 0.24 = 126.0 (answer C)