Question

Suppose that blood chloride concentration (mmol/L) has a normal distribution with mean 104 and standard deviation 5

a. What is the probability that chloride concentration equals 105? b. What is the probability that chloride concentration is less than 105?
b. What is the probability that chloride concentration differs from the mean by more than 1 standard deviation?

Answer 1

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.

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:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

a) Since normal distribution s a continuous distribution, the probability for a particular value is zero. Therefore,

`P(x =105) = 0`

b) P(chloride concentration is less than 105)

`P(x < 105) = P(z < \displaystyle(105-104)/(5)) = P(z < 0.2)`

Calculating the value from the standard normal table we have,

`P(z<0.2) = 0.579 = 57.9\%\\P( x < 105) = 57.9\%`

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