A distribution of measurements is relatively mound-shaped with mean 70 and stand

Question

A distribution of measurements is relatively mound-shaped with mean 70 and standard deviation 5. (e) What approximate proportion f the measurements will al between 65 and (a) What approximate proportion of the measurements will fall between 65 and 75? (Enter your answer to two decimal places.) (b) What approximate proportion of the measurements will fall between 60 and 80? (Enter your answer to two decimal places.) hree decimal places.) 75 (d) What approximate proportion of the measurements will be greater than 75? (Enter your answer to two decimal places.)

Explanation / Answer

a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 65) = (65-70)/5
= -5/5 = -1
= P ( Z <-1) From Standard Normal Table
= 0.15866
P(X < 75) = (75-70)/5
= 5/5 = 1
= P ( Z <1) From Standard Normal Table
= 0.84134
P(65 < X < 75) = 0.84134-0.15866 = 0.6827   ~ 68.27%
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 60) = (60-70)/5
= -10/5 = -2
= P ( Z <-2) From Standard Normal Table
= 0.02275
P(X < 80) = (80-70)/5
= 10/5 = 2
= P ( Z <2) From Standard Normal Table
= 0.97725
P(60 < X < 80) = 0.97725-0.02275 = 0.9545 ~ 95.45%
c)
P(X < 75) = (75-70)/5
= 5/5 = 1
= P ( Z <1) From Standard Normal Table
= 0.84134
P(60 < X < 75) = 0.84134-0.02275 = 0.8186 ~ 81.86%
d)
P(X > 75) = (75-70)/5
= 5/5 = 1
= P ( Z >1) From Standard Normal Table
= 0.1587   ~ 15.87%              
                  
                  
              

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