Question

For a normal curve with μ = 50 and σ = 4, how much area will be to the left of μ ?

Answer 1

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Answer 2

The area to the left of μ is 0.5 or 50%.

For a normal curve with μ = 50 and σ = 4, the area to the left of μ (the mean) can be calculated by standardizing the variable using the z-score formula: z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation.

In this case, the z-score for the mean is 0, as (50 - 50) / 4 = 0.
The area to the left of μ (which is the same as the area to the left of z = 0) can be found using a standard normal distribution table or a calculator, and it is 0.5 or 50%.

This means that 50% of the observations in a normal distribution with μ = 50 and σ = 4 are expected to be to the left of the mean (50), while the remaining 50% are expected to be to the right of the mean.

It's worth noting that the area to the left of the mean is always equal to the area to the right of the mean, as the normal distribution is symmetric around the mean.

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