Find the probability of being below 514 if the mean of a normal distribution is 474 and the standard
deviation is 32.

Step-by-step explanation:

Let x be the random variable. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 474

σ = 32

x = 514

The probability of being below 514 is expressed as P(x < 514)

For x = 514,

z = (514 - 474)/32 = 1.25

Looking at the normal distribution table, the probability value corresponding to area below the z score is 0.89

Therefore,

P(x < 514) = 0.89

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step-by-step explanation: