Question

6.A sample of n = 16 scores is obtained from a population with µ = 50 and σ = 16. If the sample mean is M = 58, then what is the z-score for the sample mean?

z = - 2.00

z = +0.50

z = +2.00

z = +8.00

7.A researcher selects a random score from a normally distributed population. What is the probability that the score will be greater than z = +1.5 and less than z = -1.5?

.07

.13

.43

.86

8.Finn receives a final exam score of 65. The class had a mean of 75 and standard deviation of 10. What percent of students in Finn's class scored lower than him?

84%

50%

34%

16%

9.A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting a score greater than 95 from this distribution?

p = 0.9332

p = 0.1587

p = 0.4332

p = 0.0668

Answer 1

This is a normal distribution question with

Sample size (n) = 16
Since we know that

P(x < 58.0)=?
The z-score at x = 58.0 is,

z = 2.0
Option C. z = +2.00

7) This is a normal distribution question with

This implies that
P(-1.5 < z < 1.5) = P(z < z2) - P(z < z1)
P(-1.5 < z < 1.5) = 0.9331927987311419 - 0.9331927987311419
P(-1.5 < z < 1.5) = 0.8664
Option D. 0.86 is correct

8) This is a normal distribution question with

P(x < 65.0)=?
The z-score at x = 65.0 is,

z = -1.0
This implies that
P(x < 65.0) = P(z < -1.0) = \textbf{0.1587}
Option D 16% is correct

9.) This is a normal distribution question with

P(x > 95.0)=?
The z-score at x = 95.0 is,

z = 1.5
This implies that
P(x > 95.0) = P(z > 1.5) = 1 - 0.9331927987311419

Option D. p = 0.0668 is correct
PS: you have to refer z score table to find the final probabilities.
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