Describe the shape of the histogram. Do the data appear to be normally distribut

Question

Describe the shape of the histogram. Do the data appear to be normally distributed. Compare the distribution of the averages to the distribution of the individual observations studied in Question 1 in terms of the center, spread, and degree of skewness. This question is 9 points so please be as specific as possile

Information from Question 1)

a) The shape of the Poisson distribution of = 0.5 is right skewed, because the value of the greatest probability distribution of x is 0, and the values decrease as x-values increase. As such, it is not symmetrical, and the values are concentrated on the left side of the graph. This tells us that at = 0.5, a randomly selected ceramic tile has little to no flaws.

b) The Poisson probability with the mean = = 0.5 when P(X=0) = 0.6065, meaning that 60.7% of randomly selected ceramic tiles will have no flaws.

c) 8.2% of boxes have all five tiles in perfect condition. Assuming that each tile is independent, the probability of all five tiles being flawless is 0.60655

Background Information:

A quality inspector at a ceramic manufacturing company inspects ceramic tiles to check for surface flaws . The number of surface flaws in ceramic tiles can be modelled by a discrete probability distribution. The ceramic tiles are shipped in boxes containing either 5 or 30 tiles. How does the number of flaws vary from tile to tile? How does the average number of flaws vary from box to box containing the same number of ceramic tiles? How does the number of ceramic tiles in a box affect the distribution of the averages?

Relative Histogram Displaying Error of the 50 Mean Samples of 30 observations Relative Frequency 0.25 0.2 0.15 0.1 0.05 0.2 0.4 0.6 0.8 Error

Explanation / Answer

The shape of the histogram is not normally distributed

We see that from 0.8 to 1 the graph has skewness

The graph has Right skewness  

The mean error is 0.5

1 standard deviation is 0.4 to 0.6

2 standard deviation is from 0.3 to 0.7

Hence option a

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