Type the correct answer in the box. Use numerals instead of words, if necessary, use / for the fraction bar. The mean of a normally distributed data as set is 12 and the standard deviation is 2.

% of the data points lies between 8 and 16.

please help!!! this is super important

Step-by-step explanation:

Let x be the random variable representing the data points in the data. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 12

σ = 2

the probability that the data points lies between 8 and 16 is expressed as

P(8 ≤ x ≤ 16)

For x = 8,

z = (8 - 12)/2 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.023

For x = 16

z = (16 - 12)/2 = 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.98

Therefore,

P(8 ≤ x ≤ 16) = 0.98 - 0.23 = 0.75

The percent of the data points that lies between 8 and 16 is

0.75 × 100 = 75%

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