Answer:
a) 0
b) 0.579 is the probability that chloride concentration is less than 105.
c) 0.32 is the probability that chloride concentration differs from the mean by more than 1 standard deviation.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 104
Standard Deviation, σ = 5
We are given that the distribution of blood chloride concentration is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) Since normal distribution s a continuous distribution, the probability for a particular value is zero. Therefore,
[tex]P(x =105) = 0[/tex]
b) P(chloride concentration is less than 105)
[tex]P(x < 105) = P(z < \displaystyle\frac{105-104}{5}) = P(z < 0.2)[/tex]
Calculating the value from the standard normal table we have,
[tex]P(z<0.2) = 0.579 = 57.9\%\\P( x < 105) = 57.9\%[/tex]
c) P(chloride concentration differs from the mean by more than 1 standard deviation)
Since it is a normal distribution, the Empirical rule shows that 68% falls within the first standard deviation, 95% within the first two standard deviations, and 99.7% within the first three standard deviations.
= 1 - P(chloride concentration within the mean by 1 standard deviation)
= 1 - 0.68 = 0.32
