Question

The heights of apricot trees in an orchard are approximated by a normal distribution model with a mean of 18 feet and a standard deviation of 1 feet. What is the probability that the height of a tree is between 16 and 20 feet

Answer 1

Answer:

0.9544

Step-by-step explanation:

We are given that mean=18 and standard deviation=1 and we have to find P(16<X<20).

P(16<X<20)=P(z1<Z<z2)

z1=(x1-mean)/standard deviation

z1=(16-18)/1=-2

z2=(x2-mean)/standard deviation

z2=(20-18)/1=2

P(16<X<20)=P(z1<Z<z2)=P(-2<Z<2)

P(16<X<20)=P(-2<Z<0)+P(0<Z<2)

P(16<X<20)=0.4772+0.4772=0.9544

The probability that the height of a tree is between 16 and 20 feet is 95.44%