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garik1379 [7]
3 years ago
13

The distribution of math SAT scores is normally distributed with a mean of 500 and a standard deviation of 90.

Mathematics
1 answer:
IrinaVladis [17]3 years ago
8 0

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:

z=\frac{x-\mu}{\sigma}

a) For x > 700

z=\frac{x-\mu}{\sigma}=\frac{700-500}{90} =2.22

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

z=\frac{x-\mu}{\sigma}=\frac{450-500}{90} =-0.56

For x = 550

z=\frac{x-\mu}{\sigma}=\frac{550-500}{90} =0.56

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

z=\frac{x-\mu}{\sigma}=\frac{680-500}{90} =2

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

z=\frac{x-\mu}{\sigma}=\frac{710-500}{90} =2.33

From the probability distribution table: P(x < 710) = P(z < 2.33) = 0.9901 = 99.01%

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