Assume the data set described is normally distributed with t

Assume the data set described is normally distributed with the given mean and standard deviation, and with n total values. Find the approximate number of data values that will fall in the given range. Mean = 420 Standard deviation = 19 n = 500 Range: 382 to 458 In this case, we expect about data values to fall between 382 and 458.

Solution

n = 500
S.D. = 19
Mean =420
range 382 to 458

The normal random variable of a standard normal distribution is called a standard score or a z-score. Every normal random variable X can be transformed into a z score via the following equation:

z = (X - ) /

where X is a normal random variable, is the mean of X, and is the standard deviation of X.

z₁ = (382-420)/19 = -2

z₂ = (458-420)/19 = 2

data values between z₁ and z₂ will be around 95% by (by 68–95–99.7 rule i.e. 95% forthis case)

95% of 500 = (95*500)/100 = 475

475 dara values to fall between 382 and 458