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
