Answer: p = 0.00714
Explanation:
Since the population standard deviation of the distribution is known, the z test ( which produces the z score) is the perfect test for finding the probability of the data set in the question.
From the question,
Population mean (u) = 114.8
Sample mean (x) = 121.5
Population standard deviation (σ) = 13.1
Sample size (n) = 23
The z score formulae is given below as
Z = x - u/σ/√n
Z = 121.5 - 114.8/(13.1/√23)
Z = 6.7/(13.1/√23)
Z = 6.7/2.731
Z = 2.45.
The question is interested in knowing the probability of mean systolic blood pressure greater than 121.5.
This implies that we are looking for the probability at which our z score is greater than 2.45: P(z>2.45)
The z score (z=2.45) has divided the distribution into two regions, z< 2.45 ( area to the left of the distribution) and z>2.45 ( area to the right of distribution).
Hence, p(z>2.45) + p(z<2.45) = 1
To get a the probability, we have to use a standard normal distribution table.
The table we have here gives probability of the distribution to the left ( that's area towards the left), hence we need to find p(z<2.45) first
From the table p(z<2.45) = 0.99286
But p(z>2.45) = 1 - p(z<2.45)
p(z>2.45) = 1 - 0.99286
p(z>2.45) = 0.00714