Question

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

Answer 1

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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

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)

$P(x < 105) = P(z < \displaystyle\frac{105-104}{5}) = P(z < 0.2)$

Calculating the value from the standard normal table we have,

$P(z$

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