Answer:
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%
