Answer: a) 0.9332, b) 0.8944
Step-by-step explanation: the probability value attached to a z score is gotten by using a z distribution table.
The z score is gotten by making use of the formulae below
Z = x - u / σ
Where x = sample mean, u = population mean and σ = population standard deviation.
a)
For our question, u = 38, σ = 12, we are to look for the z score at z ≤ 56, that's x = 56
By substituting the parameters, we have that
z ≤ 56 = 56 - 38/ 12
z ≤ 56 = 18/12
z ≤ 56 = 1.5
To get the probabilistic value, we check the normal distribution table.
The table I'm using will be giving me probabilistic value towards the left of the area.
From the table, p ( z ≤ 56) = 0.9332.
b)
Z >23 = 23 - 38/ 12
Z >23 = - 15/ 12
Z >23 = - 1.25
The probability value of this z score is towards the right of the distribution but the table I'm using is only giving probability values towards the left.
Hence Z >23 = 1 - Z<23
From the table, Z<23 = 0.1056.
Z >23 = 1 - 0.1056
Z >23 = 0.8944
