Question

The relative frequency of people who prefer cigarette is:

[A]       0.2                   [B]       40                    [C]       7                      [D]       0.035

12. A measurement x in a sample with mean 2.3 and standard deviation 1.3 has a z-score equal to -2. What is x?

[A]       -0.3                  [B]       4.6                   [C]       4.9                   [D]       -2.6     

13. Test scores of students in a statistics class have a mean of 78 and a standard deviation equal to 6. What percent of the scores are either less than 66 or greater than 90?       

[A]       approx. 5%      [B]       at least 75%     [C]       at most 25%    [D]       approx. 95%

Answer 1

1)

data is not given

2)

mean = 2.3 , s = 1.3

z value = -2

z = (x - mena)/sigma
-2 = (x - 2.3)/1.3
x = -2*1.3+ 2.3
x= -0.3

3)

Here, μ = 78, σ = 6, x1 = 66 and x2 = 90. We need to compute P(66<= X <= 90). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (66 - 78)/6 = -2
z2 = (90 - 78)/6 = 2

Therefore, we get
P(66 <= X <= 90) = P((90 - 78)/6) <= z <= (90 - 78)/6)
= P(-2 <= z <= 2) = P(z <= 2) - P(z <= -2)
= 0.9772 - 0.0228
= 0.9544

approx. 95%