A standardized test has a mean of 110 points and a standard deviation of 10 points. John scored at the 98th percentile on the test. Find his score to the nearest whole number.

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:

where,

x = score, = 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:

Thus, the score to the nearest whole number is 131.

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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

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