Determine the percentage of data with values less than or equal to 50. IF you ha

Question

Determine the percentage of data with values less than or equal to 50. IF you had used the normal distribution to approximate P(X?50) for this binomial distribution, what would you have found. Compare your answers. Would you expect them to be close? Explain.

Summary Report for p-0.50 Anderson-Darling Normality Test 0.92 0.020 50.480 4.967 24.667 Skewness 0.0194450 0.0628133 500 36.000 47.000 50.000 54.000 65.000 A-Squared P-Value Mean StDev Variance Kurtosis Minimum 1st Quartile Median 3rd Quartile Maximum 95% Confidence Interval for Mean 50.044 50.916 95% Confidence Interval for Median 36 40 48 52 56 60 64 50.000 51.000 95% Confidence Interval for StDev 4.677 5.295 95% Confidence Intervals Mean Median 50.0 50.2 50.4 50.6 50.8 51.0 T.R.HALE

Explanation / Answer

THE DISTRIBUTION IS GIVEN TO BE NORMAL

WITH MEAN = 50.48

STANDARD DEVIATION = 4.967

N = 500

WE HAVE TO CALCULATE

P(X<=50) =

For x = 50, the z-value z = (50 - 50.48) /( 4.967/SQRT(500) = -2.18

Hence P(x < 50) = P(z < -2.18), now from the z table we will take the value of z score = -2.18

And that value will be the probability required.

= [area to the left of -2.18] = 0.0146

= 1.46%

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