Question

Let x be a normally distributed continuous random variable with a mean of 213 and a...

Let x be a normally distributed continuous random variable with a mean of 213 and a standard deviation of 17. Determine the value of x such that the area to the left of x is 0.492. Round the solution to two decimal places, if necessary.

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Answer #1

solution

Using standard normal table,

P(Z < z) =0.492

= P(Z < z) = 0.492

= P(Z <-0.02 ) = 0.492

z =-0.02 Using standard normal z table,

Using z-score formula  

x= z * \sigma + \mu

x=-0.02 *17+213

x= 212.66

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