The distribution of the heights of students in a large class is roughly bell-shaped. Moreover, the average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches. Thus, the standard deviation of the height distribution is approximately equal to: a. 2
b. 3
c. 6
d. 9
e.12

a. 2

Step-by-step explanation:

According to the Empirical rule, when data is normally distributed then 95% of the lies within 2 standard deviations from mean.

Given: The distribution of the heights of students in a large class is roughly bell-shaped ( i.e. Normally distributed).

The average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches.

Then, by  Empirical rule, 68 -2(standard deviations) =62  [lower limit]

⇒ 2(standard deviations)= 68-62 = 4

⇒ standard deviations=2

Hence, correct option is a. 2

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2