Midterm review - normal and sampling distributions - solutions

# Midterm review- - Midterm Review Normal and Sampling Distributions 1 Normal distribution(section 5-3 Researchers studying the effects of a new diet

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Midterm Review – Normal and Sampling Distributions 1. Normal distribution (section 5-3) Researchers studying the effects of a new diet found that the weight loss over a one- month period by those on the diet was normally distributed with a mean of 3 kilograms and a standard deviation of 1 kilogram. Answers (a) What proportion of the dieters lost more than 4 kilograms? (1 mark) (b) What proportion of the dieters gained weight? (1 mark) (c) If a dieter is selected at random, what is the probability that the dieter lost at most 2.5 kilograms? (1 mark) Note that we are not speaking about a sample of dieters anywhere in this question. This is a plain normal distribution question. (a) 1587 . 0 3413 . 0 1 ) 1 Z 0 ( P 1 ) 1 Z ( P 1 3 4 X P ) 4 X ( P = - = < < - = = - σ μ - = (b) Gaining weight means having a negative weight loss: 0013 . 0 4987 . 0 1 ) 0 Z 3 ( P 1 ) 3 Z ( P 1 3 0 X P ) 0 X ( P = - = < < - - = - < = - < σ μ - = < (c) 3085 . 0 1915 . 0 1 ) 0 Z 5 . 0 ( P 1 ) 5 . 0 Z ( P 1 3 5 . 2 X P ) 5 . 2 X ( P = - = < < - - = - < = - < σ μ - = < 2. Normal distribution, sampling distribution for means (section 6-2) and the rules

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## This note was uploaded on 09/25/2010 for the course OMIS OMIS 1000 taught by Professor Alexandershoumarov during the Fall '09 term at York University.

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Midterm review- - Midterm Review Normal and Sampling Distributions 1 Normal distribution(section 5-3 Researchers studying the effects of a new diet

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