Suppose that a random sample of 200 light bulbs has a mean life of 600 hours and

Question

Suppose that a random sample of 200 light bulbs has a mean life of 600 hours and a standard deviation of 53 hours. Assuming that the life of light bulbs is normally distributed, what is the probability that a light bulb will have a lifetime between 441 and 759 hours?

Suppose that a random sample of 200 light bulbs has a mean life of 600 hours and a standard deviation of 53 hours. Assuming that the life of light bulbs is normally distributed, then what percentage of light bulbs will have a life between 494 and 706 hours?

According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

According to a college survey, 22% of all students work full time. Find the standard deviation for the number of students who work full time in samples of size 16.

Suppose that a random sample of 200 light bulbs has a mean life of 600 hours and a standard deviation of 53 hours. Assuming that the life of light bulbs is normally distributed, then what percentage of light bulbs will last less than 443 hours?

Suppose that a random sample of 200 light bulbs has a mean life of 600 hours and a standard deviation of 53 hours. Assuming that the life of light bulbs is normally distributed, what is the probability that a light bulb will have a lifetime between 441 and 759 hours?

Suppose that a random sample of 200 light bulbs has a mean life of 600 hours and a standard deviation of 53 hours. Assuming that the life of light bulbs is normally distributed, then what percentage of light bulbs will have a life between 494 and 706 hours?

According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

According to a college survey, 22% of all students work full time. Find the standard deviation for the number of students who work full time in samples of size 16.

Suppose that a random sample of 200 light bulbs has a mean life of 600 hours and a standard deviation of 53 hours. Assuming that the life of light bulbs is normally distributed, then what percentage of light bulbs will last less than 443 hours?

Explanation / Answer

Q1.
a.
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 ) = 600
standard Deviation ( sd )= 53
a.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 441) = (441-600)/53
= -159/53 = -3
= P ( Z <-3) From Standard Normal Table
= 0.0013
P(X < 759) = (759-600)/53
= 159/53 = 3
= P ( Z <3) From Standard Normal Table
= 0.9987
P(441 < X < 759) = 0.9987-0.0013 = 0.9973 = 99.73%
light bulb will have a lifetime between 441 and 759 hours is b/w 99.73%

b.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 494) = (494-600)/53
= -106/53 = -2
= P ( Z <-2) From Standard Normal Table
= 0.0228
P(X < 706) = (706-600)/53
= 106/53 = 2
= P ( Z <2) From Standard Normal Table
= 0.9772
P(494 < X < 706) = 0.9772-0.0228 = 0.9545 = 95.45%

light bulbs will have a life between 494 and 706 hours is 95.45%

c.
P(X < 443) = (443-600)/53
= -157/53= -2.9623
= P ( Z <-2.9623) From Standard Normal Table
= 0.0015
0.15% are less than 443

Q2.
mean ( np ) = 16 * 0.22 = 3.52
standard deviation ( npq )= 16*0.22*0.78 = 1.657
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)

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