Question

Are the data Normal? A sample of 105 rainwater specimens had mean pH 5.43; standard deviation 0.54; and five-number summary 4.33, 5.05, 5.44, 5.79, 6.81.14 (a) Compare the mean and median and also the distances of the two quartiles from the median. Does it appear that the distribution is quite symmetric? Why? (b) If the distribution is really N(5.43, 0.54), what proportion of observations would be less than 5.05? Less than 5.79? Do these proportions suggest that the distribution is close to Normal? Why?

Answer 1

TOPIC:Checking for symmetry and Normality of the given distribution.

Five number given as Minimum 4.33 5.05 median 5. 44 5.79 Maximum 6, 81 44.a3 Hene 5. 43, sd 0.54. mean mean and median ane Obsenve that, almost the same. again, median (93-meia6.79-5- 5. hר 0.39 aud =0.35 Cmedan mediay gectyy So, and ane almost the same, but hot same So, morne on Less Aymmebc Aay that the distribution is can we Undenlying diotmibution SuppaA x 14.b (u-5.49, X N

Sren we gaby P 5.05-5. 43 0.54 0.7037. 0.703 =1- Et)3 O.7592 From Nonma 1- tble values 0.2408 and, P X 5.79 X-M 5. 79-5.43 P O.54 O 7475 Sincy 81 5. 05, 835.79. we should have r (x<) 0.25 P (x C43 0.75 il

O bserwe that, the obtained propontions 0.2408 aud 0. 7275;w hich ane ane vey clase, o. 25 aud 0.75 esh e tivel profentions auggo Heuce these thal the diotnibutiona o clase to Novmal TAn&S