Question

Scores on a word reading efficiency test amongst eight-year old state school attendees have a mean of 50 and a standard deviation of 5.

Amanda Lotsofknowledge scored 2.44 standard deviations above the mean. What is her percentile rank? Show solution.

a. 52.44

b. 95.00

c. 92.20

d. 99.27

Answer 1

Solution :

Let X be a random variable which represents the scores on a word reading efficiency test amongst eight-year old state school attendees.

Given that,  μ = 50 and σ = 5

Amanda Lotsofknowledge scored 2.44 standard deviations above the mean.

Hence, Amanda's score = 50 + (5×2.44) = 62.2

Now we shall obtain percentage of attendees who have scores less than 62.2. This percentage will be the required percentile.

i.e. We have to obtain P(X < 62.2).

Using "pnorm" function of R we get, P(Z < 2.44) = 0.9927

0.9927 = 99.27%

Hence, percentile rank of Amanda is 99.27.

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