Respuesta :
Answer: his score 131 points
Step-by-step explanation:
Assuming the scores in the standardized test are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = standardized test scores.
µ = mean score
σ = standard deviation
From the information given,
µ = 110 points
σ = 10 points
Looking at the normal distribution table, the z score that corresponds to the 98 percentile is 2.06
2.06 = (x - 110)/10
Cross multiplying, it becomes
2.06 × 10 = x - 110
2.06 = x - 110
x = 20.6 + 110
x = 130.6
Approximately, x = 131
Standard deviation is defined as the measure of how a dispersed value, data, or set of number is in relation to its mean.
Given:
Mean = 110
S. Deviation = 10
From the formula of standard deviation, we have:
[tex]z = \dfrac{x - u}{\sigma}[/tex]
where,
x = score, [tex]\sigma[/tex] = standard deviation, and u = mean or raw value
Now,
z-score corresponding to 98 percentile is 2.06.
Substituting the values in the above formula, we get:
[tex]\begin{aligned} 2.06 &=\dfrac{x -110}{10}\\\\2.06 \times 10 &= x -110\\\\20.6 &= x - 110\\\\20.6 + 110 &= x\\\\130.6 &= x \end[/tex]
Thus, the score to the nearest whole number is 131.
To know more about standard deviation, refer to the following link:
https://brainly.com/question/12402189
