he mean incubation time for a type of fertilized egg kept at 100.2.°F is 20days.
ID: 3330978 • Letter: H
Question
he mean incubation time for a type of fertilized egg kept at 100.2.°F is 20days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 11 dayday. (a) What is the probability that a randomly selected fertilized egg hatches in less than 19 days? (b) What is the probability that a randomly selected fertilized egg hatches between 18 and 20 days? (c) What is the probability that a randomly selected fertilized egg takes over 21 days to hatch? (a) The probability that a randomly selected fertilized egg hatches in less than 19days is nothing.
Explanation / Answer
NORMAL DISTRIBUTION
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 ) = 20
standard Deviation ( sd )= 11
a.
P(X < 19) = (19-20)/11
= -1/11= -0.0909
= P ( Z <-0.0909) From Standard Normal Table
= 0.4638
b.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 18) = (18-20)/11
= -2/11 = -0.1818
= P ( Z <-0.1818) From Standard Normal Table
= 0.4279
P(X < 20) = (20-20)/11
= 0/11 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(18 < X < 20) = 0.5-0.4279 = 0.0721
c.
P(X > 21) = (21-20)/11
= 1/11 = 0.0909
= P ( Z >0.0909) From Standard Normal Table
= 0.4638
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