Question

For Questions 12 and 13: Let x be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam’s sociology class. After interviewing many students, it was found the x has an approximately normal distribution with mean μ = 6.8 hours and standard deviation σ = 2.1 hours.

12. Convert the x interval x ≤ 9.7 to a standard z interval. a. z ≤ 1.38 d. z ≤ -1.75 b. z ≥ 1.75 e. z ≤ -1.38 c. z ≥ 2.5   13. Convert the z interval -1.5 ≤ z ≤1 to a raw score x interval. a. 2.5 ≤ x ≤ 8.9 d. -7 ≤ x ≤ 2.5 b. 3.65 ≤ x ≤ 6.66 e. -3.65 ≤ x ≤ 8.9 c. 3.65 ≤ x ≤ 8.9

Answer 1

Solution;
Given that,
μ =6.8 hours, σ=2.1 hours, x= 9.7
12)By using the z-score formula, we get
z=(x- μ)/σ
x ≤ 9.7= [(x- μ)/σ]≤[(9.7 - 6.8)/2.1]
=z ≤ 1.38
Answer: a) z ≤ 1.38
13) solution:
-1.5 ≤ z ≤1
By using the z-score formula, we can calculate value of x as,
z=(x- μ)/σ

When z= -1.5
-1.5= (x- 6.8)/2.1
x=[ (-1.5)×2.1]+6.8
x= -3.15 + 6.8
=3.65
Similarly,when z=1
1= (x- 6.8)/2.1
x=[ (1)×2.1]+6.8
x= 2.1+ 6.8
=8.9

Therefore,
3.65 ≤ x ≤ 8.9
Answer: c. 3.65 ≤ x ≤ 8.9