Calculate Z-score, probability, percentile and normal distribution values.
Foundation of statistics
Normal distribution (Gaussian distribution) is the most common probability distribution in nature and social sciences. It is bell-shaped and symmetric around the mean. Many natural phenomena (height, weight, intelligence) follow normal distribution. Z-Score and interpretation: Z-score = (X - μ) / σ. Z=0 means at the mean, Z=1 is 1 standard deviation above mean, Z=-2 is 2 standard deviations below mean. In IQ tests, mean is 100, standard deviation is 15. Someone with IQ 115 has Z-score = 1. Applications and examples: Quality control (product measurements), standardizing test scores (comparing different exams), risk management and finance (stock returns), health sciences (blood values, diagnostic tests), significance testing in scientific research.
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Z-score shows how many standard deviations a value is from the mean. Z=0 is the mean, Z=1 is 1 standard deviation above, Z=-1 is 1 standard deviation below.
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