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In: Statistics and Probability

Q4) The temperature degrees of certain set of cities are normally distributed. The cities are classified...

Q4) The temperature degrees of certain set of cities are normally distributed. The cities are classified into three categories. The lowest 12.92% are in category I, The highest 10.38% are in Category III, and the other cities are in category II, with degrees between α and β.

i. Find the z- scores of α and β.

ii. Given the mean temperature degrees is 6.84 and the standard deviation is 0.25. Find the values of α and β

Solutions

Expert Solution

4.

Suppose, random variable X denotes temperature degree of a city.

(i)

By given data,

   [Using R-code 'qnorm(0.1292)']

Again,

[Using R-code 'qnorm(0.8962)']

Hence, z-scores of and are -1.130181 and 1.260192 respectively.

(ii)

Hence, values of and are 6.557455 and 7.155048 respectively.

orchestra answered 1 year ago
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