Prefer calculator answer A large part of the luggage market is made up of overni
ID: 3177846 • Letter: P
Question
Prefer calculator answer
A large part of the luggage market is made up of overnight bags. These bags vary by weight, exterior appearance, material, and size. Suppose the volume of overnight bags is normally distributed with mean mu = 1750 cubic inches and standard deviation sigma = 250 cubic inches. A random sample of 15 overnight bags is selected, and the volume of each is found. a. Find the distribution of X bar. b. What is the probability that the sample mean volume is more than 1800 cubic inches? c. What is the probability that the sample mean volume is within 100 cubic inches of 1750? d. Find a symmetric interval about 1750 such that 95% of all values of the sample mean volume lie in this interval.Explanation / Answer
a. Here it is given that population is normal distribution so as per central limit theorem sample mean will also be normally distributed with mean =1750 and sd=sd/sqrt(n)=250/sqrt(15)=64.55
c. P(xbar>1800)=P(z>1800-1750/64.55)=P(z>0.77)=0.5-P(0<=z<=0.77)=0.5-0.2794=0.2206
c. P(-100/64.55<z<100/64.55)=P(-1.55<z<1.55)=P(0<=z<=1.55)+P(-1.5<=z<=0)=0.4394+0.4394=0.8789
d. Here we need to find P(-z1<z<z2)=0.95
using z table we get z=+/-1.96
now z value=xbar-mean/sd=x-1750/64.55
hence xbar1=-1.96*64.55+1750=1623.482
and xbar2=1.96*64.55+1750=1876.518