Question

ou may need to use the appropriate appendix table to answer this question.

Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm).† Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm.

(a)

What is the probability that a Dutch male is shorter than 177 cm? (Round your answer to four decimal places.)

(b)

What is the probability that a Dutch male is taller than 196 cm? (Round your answer to four decimal places.)

(c)

What is the probability that a Dutch male is between 174 and 192 cm? (Round your answer to four decimal places.)

(d)

Out of a random sample of 1,000 Dutch men, how many would we expect to be taller than 188 cm? (Round your answer to the nearest integer.)

men

Answer 1

Solution :

Given that ,

a) P(x < 177)

= P[(x - ) / < (177 - 183) / 10.5]

= P(z < -0.57)

Using z table,

= 0.2843

b) P(x > 196 ) = 1 - p( x< 196)

=1- p P[(x - ) / < (196 - 183) / 10.5]

=1- P(z < 1.24)

= 1 - 0.8925

= 0.1075

c) P( 174 < x < 192) = P[(174 - 183)/ 10.5 ) < (x - ) /  < (192 - 183) / 10.5 ) ]

= P(-0.86 < z < 0.86 )

= P(z < 0.86) - P(z < -0.86)

Using z table,

= 0.8051 - 0.1949

= 0.6102

d) P(x > 188 ) = 1 - p( x< 188)

=1- p P[(x - ) / < (188 - 183) / 10.5]

=1- P(z < 0.48)

= 1 - 0.6844

= 0.3156

= 1000 * 0.3156 = 315.6

= 316 men