(c) (2 pts) Find the probability the student will answer correctly at most 5 of
ID: 2925928 • Letter: #
Question
(c) (2 pts) Find the probability the student will answer correctly at most 5 of the questions. Use the odf to answer this quesition (d)(2 pts) Let Y = 10-X. In words, what does Y represent? (e) (2 pts) Use the cdf to find P(2-Y-5). (Hint: Just plug in Y = 10-X.) Question 4 (10 points) The resistence for resistors of a certain type is a random variable X having the nor mal distribution with mean 9 ohms and standard deviation 0.4 ohms. A resistor is (a)(5 pts) What is the probability that a randomly chosen resistor is acceptable? (b)(5 pts) What is the probability that out of four randomly and independently acceptable if its resistance is between 8.6 and 9.8 ohms. (Hint: Check normal table in appendix or use R.) selected resistors, two are acceptable? (Hint: Link this to the interpretation of a binomial random variable.)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 ) = 9
standard Deviation ( sd )= 0.4
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 8.6) = (8.6-9)/0.4
= -0.4/0.4 = -1
= P ( Z <-1) From Standard Normal Table
= 0.1587
P(X < 9.8) = (9.8-9)/0.4
= 0.8/0.4 = 2
= P ( Z <2) From Standard Normal Table
= 0.9772
P(8.6 < X < 9.8) = 0.9772-0.1587 = 0.8186
b)
X ~ B(4,0.8186)
P( X = 2 ) = ( 4 2 ) * ( 0.9772^2) * ( 1 - 0.9772 )^2
= 0.00298
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