Answer:
a) 1.39%
b) 42.26%
c) 97.72%
d) 7.78%
e) 99.01%
Step-by-step explanation:
mean (μ) = 500, standard deviation (σ) = 90
The z score is used to measure the amount by which the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For x > 700
[tex]z=\frac{x-\mu}{\sigma}=\frac{700-500}{90} =2.22[/tex]
From the probability distribution table:
P(x > 700) = P(z > 2.22) = 1 - P(z < 2.22) = 1 -0.9861 = 0.0139 = 1.39%
b) For x = 450
[tex]z=\frac{x-\mu}{\sigma}=\frac{450-500}{90} =-0.56[/tex]
For x = 550
[tex]z=\frac{x-\mu}{\sigma}=\frac{550-500}{90} =0.56[/tex]
From the probability distribution table:
P(450< x < 550) = P(z < 0.56) - P(z < -0.56) = 0.7123 - 0.2877 = 0.4246 = 42.46%
c) For x < 680
[tex]z=\frac{x-\mu}{\sigma}=\frac{680-500}{90} =2[/tex]
From the probability distribution table:
P(x < 680) = P(z < 2) = 0.9772 = 97.72%
d) From the probability distribution table: P(z < -1.42) = 0.0778 = 7.78%
e) c) For x = 710
[tex]z=\frac{x-\mu}{\sigma}=\frac{710-500}{90} =2.33[/tex]
From the probability distribution table: P(x < 710) = P(z < 2.33) = 0.9901 = 99.01%
