Question

Among all monthly bills from a certain credit card company, the mean amount billed was $465 and the standard deviation was $300. In addition, for 15% of the bills, the amount billed was greater than $1000. A sample of 900 bills is drawn. What is the probability that the average amount billed on the sample bills is greater than $500? (Round the final answer to four decimal places.)

Answer 1

here as sample size is greater than 30, from central limit thoerem we can use normal approximation of above model

for normal distribution z score =(X-μ)/σx
here mean=       μ=	465
std deviation   =σ=	300.0
sample size       =n=	900
std error=σx̅=σ/√n=	10.00

  probability that the average amount billed on the sample bills is greater than $500:

probability =

P(Xbar>500)

=

P(Z>3.5)=

1-P(Z<3.5)=

1-0.9998=

0.0002