Question

A distribution of measurements is relatively mound-shaped with mean 30 and standard deviation 5.

(a) What proportion of the measurements will fall between 25 and 35?

(b) What proportion of the measurements will fall between 20 and 40?

(c) What proportion of the measurements will fall between 20 and 35?

(d) If a measurement is chosen at random from this distribution, what is the probability that it will be greater than 35?

Answer 1

Solution :

Given that ,

mean = = 30

standard deviation = = 5

a) P(25 < x < 35) = P[(25 - 30)/ 5) < (x - ) /  < (35 - 30) / 5 ) ]

= P(-1.00 < z < 1.00)

= P(z < 1.00) - P(z < -1.00)

Using z table,

= 0.8413 - 0.1587

= 0.6826

b) P(20 < x < 40) = P[(20 - 30)/ 5) < (x - ) /  < (40 - 30) / 5 ) ]

= P(-2.00 < z < 2.00)

= P(z < 2.00) - P(z < -2.00)

Using z table,

= 0.9772 - 0.0228

= 0.9544

c) P(20 < x < 35) = P[(20 - 30)/ 5) < (x - ) /  < (35 - 30) / 5 ) ]

= P(-2.00 < z < 1.00)

= P(z < 1.00) - P(z < -2.00)

Using z table,

= 0.8413 - 0.0228

= 0.8185

d) P(x > 35) = 1 - p( x< 35)

=1- p P[(x - ) / < (35 - 30) / 5]

=1- P(z < 1.00 )

= 1 - 0.8413

= 0.1587