SHOW EVIDENCE OF HOW YOU DO EACH PROBLEM 1) Based on EPA tests of a new car, eng
ID: 3318670 • Letter: S
Question
SHOW EVIDENCE OF HOW YOU DO EACH PROBLEM 1) Based on EPA tests of a new car, engineers have found that the miles per gallon readings are normally distributed, with a mean of 32 MPG and a standard deviation of 3.5 MPG. (13 points) o) What is the probability that a randomly selected car's MPG rating exceeds 34 MPG? (2 points) b) If a random sample of ten cars is taken, what is the standard deviation of the sample mean for this sample size? (3 points) What is the probabilty that the mean MPG for the sample taken in part b) is greater than 34 MPG? (3 points) c) d) Suppose that 20 cars were included in the sample. What effect does this have on the standard deviation of the sample means? (2 points) e) What is the probability that the mean MPG for the cars in the sample from part d) is greater than 34 MPG? (3 points)Explanation / Answer
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 32
standard Deviation ( sd )= 3.5
a.
P(X > 34) = (34-32)/3.5
= 2/3.5 = 0.5714
= P ( Z >0.5714) From Standard Normal Table
= 0.2839
b.
mean of the sampling distribution ( x ) = 32
standard Deviation ( sd )= 3.5/ Sqrt ( 10 ) =1.1068
sample size (n) = 10
c.
P(X > 34) = (34-32)/3.5/ Sqrt ( 10 )
= 2/1.107= 1.807
= P ( Z >1.807) From Standard Normal Table
= 0.0354
d.
mean of the sampling distribution ( x ) = 32
standard Deviation ( sd )= 3.5/ Sqrt ( 20 ) =0.7826
sample size (n) = 20
it is decreased
e.
P(X > 34) = (34-32)/3.5/ Sqrt ( 20 )
= 2/0.783= 2.5555
= P ( Z >2.5555) From Standard Normal Table
= 0.0053
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