Question

A widely used measure of infant development is the Psychomotor Development Index (PDI). Since the PDI has been used so frequently, we have a pretty good idea of the population mean and population standard deviation for scores on the PDI. The population mean is 100, and the population standard deviation is 15. Given this, what is the probability that: a) In a sample of 100 infants, the sample mean PDI score is 101 or greater. b) In a sample of 100 infants, the sample mean PDI score is 98 or less. c) In a sample of 36 infants, the sample mean PDI score is 98 or less.

Answer 1

Sol eiven Imfent dewlgpmad widel used measune A in he pychomotos developrneut ndex (pr) given hy population l00 mean stardasd deviabion 6) 5 we need t fird Sample 10e s de mean 1.e, P CI01) X-lh we hnow that l0/- loo 15/ 100 P(Xz 10) 1P 53 P(z 2 Pz0.6666) using standard Moomal 2- bable 0.2525138

= 0.2525138 (b) ample Sagaple 0 Infents, the (00 mean PDI SCove 98 os les Know that = l0o, 6:15 he pt)-P (x-A 15/T00 -2 (10) P lz 15 PC -20 z -3333) 0.0912167 sample Infaut ple mean Sam 100 0. 0912167 PD SCore s 98 (o) les Sample 6 Infauts, Samle mean_pon we know that - l00, = 15, have to take Hene n 36 we he Pnow that

Х.de 98-lo0 P 153 -2(6) 15 2 1 table, 2- using standa Novrmral 0 21/8554 Sample 36 Irfads, sample mean SCose 0.2118554 is 98 (o) less