Could someone do this problem step by step please? Thank you! Students in a mate
ID: 3131645 • Letter: C
Question
Could someone do this problem step by step please? Thank you!
Students in a materials lab are required to experimentally determine the heat conductivity of aluminum. If student-derived values are normally distributed about a mean of .5 (cal/(cm)(sec)(degree C)) with standard deviation of .03, evaluate the probability that an individual student will obtain a conductivity from .48 to .52. If student values have the mean and standard deviation given in (a), evaluate the probability that a class of 25 students will produce a sample mean conductivity from .48 to .52. If student values have the mean and standard deviation given in (a), evaluate the probability that at least 2 of the next 5 values produced by students will be in the range from .48 to .52.Explanation / Answer
MEAN = 0.5
STANDARD DEV = 0.03
A) P(0.48<X<0.52) =
For x = 0.48 , z = (0.48- 0.5) / 0.03 = -0.66 and for x = 0.52, z = (0.52 - 0.5) / 0.03 = 0.66
Hence P(0.48 < x < 0.52) = P(-0.66 < z < 0.66) = [area to the left of z = 0.66] - [area to the left of -0.66]
= 0.7454 - 0.2546 = 0.4908
B) IN THIS PART AGAIN WE WILL HAVE THE SAME PROBABILITY OF 0.4908
AS THE CLASS SIZE WILL NOT HAVE ANY EFFECT.
C) OUT OF 5 WE NEED AT LEAST TWO
P(ATLEAST 2) = 1- P(0) - P(1)
P(0) = 5C0*(0.49)^0*(0.51)^5 = 0.034
P(1) = 5C1*(0.49)^1*(0.51)^4 = 0.165
TOTAL WILL BE 0.199
HENCE P(AT LEAST 2) = 1 -0.199 = 0.801