Question

Scores on a standardized test are normally distributed with a mean of 480 and a standard deviation of 90. What proportion of the scores are above 700? What is 25th percentile of the score? If Someone’s score is 600, what percentile is she on? What proportion of the score are between 420 and 520?

Answer 1

Answer:

Step-by-step explanation:

Since the scores on the standardized test are approximately normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = test scores.

µ = mean score

σ = standard deviation

From the information given,

µ = 480

σ = 90

1) The proportion of scores above 700 is expressed as

P(x > 700) = 1 - P(x ≤ 700)

For x = 700,

z = (700 - 480)/90 = 2.44

Looking at the normal distribution table, the probability corresponding to the z score is 0.99

P(x > 700) = 1 - 0.99 = 0.01

the proportion of scores above 700 is 0.01

2) For the 25 percentile, z = - 0.67. Therefore,

- 0.67 = (x - 480)/90

90 × - 0.67 = x - 480

- 60.3 = x - 480

x = - 60.3 + 480

x = 419.7

3) if Someone’s score is 600, then

z = (600 - 480)/90 = 1.33

From the table, the percentileis

0.91 × 100 = 91%

4) For x = 420,

z = (420 - 480)/90 = - 0.67

The proportion is 0.25

For x = 520,

z = (520 - 480)/90 = 0.44

The proportion is 0.67

The proportion of the score between 420 and 520 is

0.67 - 0.25 = 0.42