Answer :
Answer:
0.0579 is the probability that mean systolic blood pressure is between 119 and 122 mm Hg for the sample.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 114.8 mm Hg
Standard Deviation, σ = 13.1 mm Hg
Sample size = 23
We are given that the distribution of systolic blood pressures is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
Standard error due to sampling:
[tex]\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{13.1}{\sqrt{23}} = 2.731[/tex]
P(blood pressure is between 119 and 122 mm Hg)
[tex]P(119 \leq x \leq 122) = P(\displaystyle\frac{119 - 114.8}{2.731} \leq z \leq \displaystyle\frac{122-114.8}{2.731}) = P(1.537 \leq z \leq 2.636)\\\\= P(z \leq 2.636) - P(z < 1.537)\\= 0.9958 - 0.9379 = 0.0579= 5.79\%[/tex]
[tex]P(119 \leq x \leq 122) = 5.79\%[/tex]
0.0579 is the probability that mean systolic blood pressure is between 119 and 122 mm Hg for the sample.