Question

A certain type if ant has a length which is approximately normally distributed with mean 4 millimeters (mm) and standard deviation 2 mm.   What is the probability that a random sample of 16 of these ants will have mean length between 3.5 and 4.5 mm?

*Please explain clearly so I can follow along!*

Answer 1

Solution :

Given that ,

mean =   = 4

standard deviation = = 2

n = 16

= 4

=  / n= 2 / 16=0.5

P(3.5<     < 4.5) = P[(3.5 - 4) / 0.5< ( - ) /   < (4.5 - 4) /0.5 )]

= P( -1< Z <1 )

= P(Z < 1) - P(Z < -1)

Using z table

=0.8413 - 0.1587

probability= 0.6826