Question

A normally distributed data set with a mean of 35 and a standard deviation of 5 is represented by the normal curve. What is the z–score corresponding to 45?

Answer 1

Answer:

The z–score corresponding to 45 is z=2.

Step-by-step explanation:

We have a random variable X represented by a normal distribution, with mean 35 and standard deviation 5.

The z-score represents the value X relative to the standard normal distribution. This allows us to calculate probabilities for any given normal distribution with the same table.

The z-score for X=45 can be calculated as:

$z=\dfrac{X-\mu}{\sigma}=\dfrac{45-35}{5}=\dfrac{10}{5}=2$

The z–score corresponding to 45 is z=2.