Question

5. Suppose a set of math test scores is normally distributed with a mean of 100 (you do not need to know the standard deviation to answer this question, but you may find it helpful to plug in a standard deviation of your choice). If you randomly select a sample of scores from this distribution, which of the following probabilities is higher? Explain your answer. • The probability of the sample mean falling between 100 and 105 with a sample of 25 scores. • The probability of the sample mean falling between 100 and 105 with a sample of 36 scores.

Answer 1

u=100 let assume 8:5 a) n=25 P11004x4105) Mx45100 St Joan .P( 100-100 24 105.100) Ploc245) = P(225) - P(220) = 0.9994-0.g. 50.4989 b) 1:36 My=U1=600 POR: 0.83 (100LX<105): R 100-100 033 , 105-10o 0.83 / - Ploaza 602) (p-value from 2-table) -- P(24@6.02) - P1260) : 1-0.5 F015 Probability of 6 is higher than @ because in @ in' is higher than @ Standard deviation is inversly proportinal to in' E if nord