The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .2 inches. What is the probability that a randomly selected sample of 4 sheets will have an average length of less than 29.9 inches long?
Accepted Solution
A:
Answer: 0.0668Step-by-step explanation:Given : The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.i.e. [tex]\mu=30.5[/tex] and [tex]\sigma=0.2[/tex]Let x denotes the lengths of aluminum-coated steel sheets.Then the probability that a randomly selected sample of 4 sheets will have an average length of less than 29.9 inches long will be :-[tex]P(x<29.9)=P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{29.9-30.05}{\dfrac{0.2}{\sqrt{4}}})\\\\=P(z<-1.5)=1-P(z<1.5)\ \ [\because\ P(Z<-z)=1-P(Z<z)][/tex][tex]=1-0.9332= 0.0668 [/tex] [by using the z-value table ]Hence, the required probability = 0.0668