The Normal Distribution: z-Scores & the Standard Normal CDF (University)
Free printable university statistics worksheet on normal probabilities via z-scores and the standard normal CDF Phi(z), computed with the Zelen & Severo polynomial approximation (Abramowitz & Stegun 26.2.17), not the empirical rule.
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Probability & Statistics · Math worksheet
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Math
The Normal Distribution: z-Scores & the Standard Normal CDF
Standardise with z = (x - mu)/sigma (2 decimal places), then evaluate probabilities with the standard normal CDF Phi(z). Round probabilities to 4 decimal places.
- 1.Weights of machine-filled flour bags follow N(mu = 1003, sigma = 7) in g. Find P(994.6 < X < 1000.9). Use the standard normal CDF Phi and round to 4 decimal places.
- 2.Scores on a standardised exam follow N(mu = 544, sigma = 56) in points. Find the probability that a randomly chosen value is greater than 555.2 points. Use the standard normal CDF Phi and round to 4 decimal places.
- 3.Adult heights in a population follow N(mu = 167, sigma = 8) in cm. Find the probability that a randomly chosen value is greater than 151.8 cm. Use the standard normal CDF Phi and round to 4 decimal places.
- 4.Systolic blood pressure of adults follow N(mu = 116, sigma = 11) in mmHg. Find P(97.3 < X < 110.5). Use the standard normal CDF Phi and round to 4 decimal places.
- 5.Weights of machine-filled flour bags are normally distributed with mean 1009 g and standard deviation 7 g. Find the z-score of a value of 1020.2 g, rounded to 2 decimal places.
- 6.Scores on a standardised exam follow N(mu = 509, sigma = 70) in points. Find the probability that a randomly chosen value is less than 635 points. Use the standard normal CDF Phi and round to 4 decimal places.
- 7.Weights of machine-filled flour bags follow N(mu = 999, sigma = 6) in g. Find the probability that a randomly chosen value is greater than 1003.2 g. Use the standard normal CDF Phi and round to 4 decimal places.
- 8.Systolic blood pressure of adults follow N(mu = 124, sigma = 8) in mmHg. Find the probability that a randomly chosen value is greater than 135.2 mmHg. Use the standard normal CDF Phi and round to 4 decimal places.
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