Question

We’ve established that heights of 10-year-old boys vary according to a Normal distribution with μ = 140 cm and σ = 5 cm.

What proportion is between 150 and 140 cm?

	a.	68%
	b.	50%
	c.	97.72%
	d.	47.72%

Answer 1

Solution :

Given that ,

mean = $\mu$ = 140

standard deviation = $\sigma$ = 5

P(140< x <150 ) = P[(140 - 140) / 5< (x - $\mu$ ) / $\sigma$< (150 - 140) / 5)]

= P( 0< Z < 2)

= P(Z < 2) - P(Z < 0)

Using z table   

= 0.9772 - 0.5

=0.4772

=47.72%