Q: If the scores for a test have a mean of 70 and a standard deviation of 12 what percentage of scores will fall below 50?

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T score is usually used when the sample size is below 30 and/or when the population standard deviation is unknown.

The area between the mean and 1 standard deviation above or below the mean is about 0.3413 or 34.13%

X = 50 => Z = (50 - 70)/12 = -20/12 = -1.33 So prob(X < 50) = Prob(Z < -1.33...) = 0.091

There must be a formula, but in the mean time there is a handy site that does it for you. [See related link below for the converter]

A single number, such as 478912, always has a standard deviation of 0.

Standard deviation calculation is somewhat difficult.Please refer to the site below for more info

A single number, such as 478912, always has a standard deviation of 0.

There are approximately 16.4% of students who score below 66 on the exam.

Suppose the random variable, X, that you are studying, has a mean = m, and standard deviation (sd) = s. Then z = 1.33 is equivalent to saying that(x - m)/s = 1.33 or that your observed value is greater than the mean by 1.33 times the sd.

Yes. If the variance is less than 1, the standard deviation will be greater that the variance. For example, if the variance is 0.5, the standard deviation is sqrt(0.5) or 0.707.

Assuming a normal distribution, the proportion falling between the mean (of 8) and 7 with standard deviation 2 is: z = (7 - 8) / 2 = -0.5 → 0.1915 (from normal distribution tables) → less than 7 is 0.5 - 0.1915 = 0.3085 = 0.3085 x 100 % = 30.85 % (Note: the 0.5 in the second sum is because half (0.5) of a normal distribution is less than the mean, not because 7 is half a standard deviation away from the mean, and the tables give the proportion of the normal distribution between the mean and the number of standard deviations from the mean.)

34.1% of the data values fall between (mean-1sd) and the mean.