Question

A set of data whose histogram is extremely skewed yields a mean and standard deviation of 70 and 12, respectively. What is the minimum proportion of observations that:

A) Are between 46 and 94?

B) Are between 34 and 106?

Answer 1

Solution :

Given that ,

mean = = 70

standard deviation = = 12

Are between 46 and 94

P( 46< x < 94) = P[(46 -70)/ 12) < (x - ) /  < (94-70) /12 ) ]

= P( -2< z < 2)

= P(z <2 ) - P(z <-2 )

Using standard normal table

= 0.9772 -0.0228 = 0.9545

Probability = 0.9545

Proportion = 0.9545

b) Are between 34 and 106

P( 34< x < 106) = P[(34 -70)/ 12) < (x - ) /  < (106-70) /12 ) ]

= P( -3< z < 3)

= P(z < 3 ) - P(z <-3 )

= 0.9987-0.0013= 0.9974

Probability = 0.9973

Proportion = 0.9973