Answer:
Option 3 and 4.
Step-by-step explanation:
The z score shows by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \ \sigma=standard\ deviation[/tex]
Given that mean (μ) = 82, standard deviation (σ) = 5
1) For x = 74:
[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{74-82}{5} =-1.6[/tex]
Option 1 is incorrect
2) For x < 87
[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{87-82}{5} =1[/tex]
From the normal distribution table, P(x < 87) = P(z < 1) = 0.8413 = 84.13%
Option 2 is incorrect
3) For x = 95:
[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{95-82}{5} =2.6[/tex]
Option 3 is correct
4) For x < 77
[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{77-82}{5} =-1[/tex]
From the normal distribution table, P(x < 77) = P(z < -1) = 0.16 = 16%
Option 4 is correct
5) For x > 92
[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{92-82}{5} =2[/tex]
From the normal distribution table, P(x > 92) = P(z > 2) = 1 - P(z < -2) = 1 - 0.9772 = 0.0228 = 2.28%
Option 5 is incorrect
