In: Statistics and Probability
Technology advancements have become a driving force for national and economic growth to transact across the global. Service providers have become so alarmed with the rate at which customers are able to download a web page. In one of the optic fiber survey, it was noted that the most customers tend to experience a mean download time of a resource web page is normally distributed to 8.5 seconds. After analysis by the census office, the data obtained had a standard deviation of 4.5 seconds.
Technology advancements have become a driving force for national and economic growth to transact across the global. Service providers have become so alarmed with the rate at which customers are able to download a web page. In one of the optic fiber survey, it was noted that the most customers tend to experience a mean download time of a resource web page is normally distributed to 8.5 seconds. After analysis by the census office, the data obtained had a standard deviation of 4.5 seconds.
As the distribution is normal we can convert x into z.
i.What probability of page downloads take less than 5 seconds?
Here we need to find P(x<5)=
ii.What is the probability that the download time will be between 5 and 11 seconds?
Here we need to find P(5<x<11)=
iii.Here we need to find x such that P(x<X)=0.25
X=(0.4926*4.5)+8.5=10.72
X=10.72
iv.If 10 downloads are randomly selected, how many downloads are expected to take more than 12 seconds
Here first we need to find P(x>12)=
Out of 10 downloads 0.218*10=2.18 are expected to take more than 12 seconds.
v.What is the probability that the download time will be between 10 and 12 seconds
Here we need to find P(10<x<12)=
P(10<x<12)=0.1513