Question

Suppose X∼N(12.5,1.5), and x=11. Find and interpret the z-score of the standardized normal random variable.\

Answer 1

Answer:

x= 3.5 is -2. The mean is 6.5.

z score to the left is 2

Step-by-step explanation:

X is a normally distributed random variable with μ=6.5 (mean) and σ=1.5 (standard deviation). To calculate the z-score,

z=x−μσ=3.5−6.51.5=−31.5=−2

This means that x=3.5 is two standard deviations (2σ) below or to the left of the mean. This makes sense because the standard deviation is 1.5. So, two standard deviations would be (2)(1.5)=3, which is the distance between the mean (μ=6.5) and the value of x (3.5).

Answer 2

Answer:

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Step-by-step explanation:

Using the normal distribution, it is found that x = 3.5 has a z-score of -2, which means that it is 2 standard deviations below the mean.

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In a normal distribution with mean  and standard deviation , the z-score of a measure X is given by:

The z-score measures how many standard deviations the measure X is from the mean, above or below.  

X∼N(6.5,1.5), which means that .

The measure is

The z-score is:

The measure x = 3.5 has a z-score of -2, which means that it is 2 standard deviations below the mean.