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Suppose that the scores of architects on a particular creativity test are normally distributed with a mean of

297

and a standard deviation of

22.

Using a normal curve​ table, find the top and bottom scores for each of the following middle percentages of architects.

​(a)

53​%

​(b)

90​%

​(c)

96​%

Answer 1

Let X denotes the score of architects on a particular creativity test.

X ~ Normal(297,22²)

Using Minitab software, (Graph -> Probability distribution plots -> View probability -> Distribution : Normal), we get the following output -

a)

Distribution Plot Normal, Mean=297, StDev=22 0.020 0.53 0.015 Density 0.005 0.0003 281.1 297 312.9 X

bottom score = 281.1

top score = 312.9

b)

Distribution Plot Normal, Mean=297, StDev=22 0.020 09 0.015 Density 0.010 0.005 0.000 260.8 297 333.2

bottom score = 260.8

top score = 333.2

c)

Distribution Plot Normal, Mean=297, StDev=22 0.020 0.96 0.015 Density 0.005 0.000 251.8 297 342.2

bottom score = 251.8

top score = 342.2