Consider the following dataset 15 24 24 30 3131 38 394548 48

Consider the following dataset: 15, 24, 24, 30, 31,31, 38, 39,45,48, 48 and 50. When forming a normal probability plot, what is found on the Y-Axis? Determine the vertical plotting position for the 7th observation. What percent of the population is less than or equal to a value of 39? What is one way to determine if the population is normally distributed?

Solution

A. when forming a normal probability plot on Y axis we plot the probability. that is the Y axis is a scale with range 0 to 1

B. let X~normal distribution with mean as that of sample mean and variance as that of sample variance.

sample mean=35.25

sample varance=126.0227

so P[X=7] =0.001498 [answer] where X~N(35.25,126.0027)

C) P[X<39]=P[(X-35)/sqrt(126.0027)<(39-35.25)/sqrt(126.0027)]=P[Z<0.334072]=0.6307387   [answer]   where Z~N(0,1)

D) we know that normal distribution is a symmetric distribution.

so one way to determine if the population is normally distributed or not is to check whether the sample mean,sample median and sample mode are equal or very close enough.