Question

Using Excel The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from 5.8 to 6.8 years. We randomly select one first grader from the class.

1. Define the random variable. X = _________
2. X ~ ________
3. f(x) = _________
4. μ = _________
5. σ = _________
6. Find the probability that she is over 6.5 years old.
7. Find the probability that she is between four and six years old.
8. Find the 70^th percentile for the age of first graders on September 1 at Garden Elementary School.

Answer 1

(Note:excel does not have specific function for uniform distribution , these can be solved by simple arithmatic)

X = age of a first grader on September 1 at Garden Elementary School

X~ U(5.8,6.8)

f)X)=1/(b-a) =1/(6.8-5.8 )=1

mean μ=(a+b)/2 =

6.3

standard deviation σ=(b-a)/√12=(6.8-5.8)/sqrt(12)=

0.2887

a)

probability that she is over 6.5 years old:

P(X>6.5)=-P(X<6.5)=1-(6.5-5.8)/(6.8-5.8)=0.3

b)

probability that she is between four and six years old :

P(4<X<6) =(6-5.8)/(6.8-5.8) =0.2

c)

pth percentile =a+p*(b-a)/100

therefore 70th percentile =5.8+70*(6.8-5.8)/100=6.5 years