Question

Suppose that blood chloride concentration (mmol/L) follows a normal distribution with a mean of 109 and a standard deviation of 5.

(a) Calculate the following probabilities, rounding your answers to four decimal places:
i. What is the probability that chloride concentration equals 110?
ii. What is the probability that chloride concentration is less than 110?
iii. What is the probability that chloride concentration is at most 110?

Answer 1

To calculate the probabilities, we can use the formula for the standard normal distribution. Z = (X - µ) / σ, where Z is the z-score, X is the value we want to find the probability for, µ is the mean, and σ is the standard deviation.

Step-by-step explanation:

a. i. To calculate the probability that chloride concentration equals 110, we can use the formula for the standard normal distribution. The formula is given by:

Z = (X - µ) / σ

Where:

• Z is the z-score
• X is the value we want to find the probability for
• µ is the mean of the distribution
• σ is the standard deviation of the distribution

In this case, X = 110, µ = 109, and σ = 5. Plugging these values into the formula, we get:

Z = (110 - 109) / 5 = 0.2

Now, we can use a z-table or a calculator to find the probability associated with a z-score of 0.2. The probability is approximately 0.5793.

a. ii. To calculate the probability that chloride concentration is less than 110, we need to find the probability associated with a z-score less than 0.2. Using a z-table or a calculator, we find that the probability is approximately 0.5793.

a. iii. To calculate the probability that chloride concentration is at most 110, we need to find the probability associated with a z-score less than or equal to 0.2. Using a z-table or a calculator, we find that the probability is approximately 0.5793.