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Mr. Templin promised that if we all score at least 50% on the test, we will pass. Sadly, the test was a killer, and he said the mean was 46% with a standard deviation of 4%. If the scores were normally distributed, what percentage of the class passed?

Sagot :

oladayoademosu

The percentage of the class that passed is 16%.

Since we require at least 50% to pass the test and the mean of test is X = 46 % and its standard deviation is σ = 4%, we need to find how many standard deviations away from the mean contain 50% or more.

Now, everything below 46% which is the mean failed and this is 50 % of the class, if the scores were normally distributed,

Number of standard deviations away from the mean

We need to find how many standard deviations away from the mean is 50 %.

So, n = (X - μ)/σ where

  • X = score = 50 %,
  • μ = mean = 46 % and
  • σ = standard deviation = 4 %

So, n = (X - μ)/σ

n = (50% - 46%)/4%

n = 4%/4%

n = 1

So, at 1 standard deviation away from the mean, there are 34% of the values contanined.

Percentage of class who failed the test

So, the percentage of the class less than 50% is 50% + 34% = 84 %.

Percentage of class who passed the test

The percentage of the class greater than 50% is 100% - 84% = 16%

So, the percentage of the class that passed is 16%.

Learn more about normal distribution here:

https://brainly.com/question/16943251

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