Search & Filtering
A random sample of 25 observations was drawn from a normal population whose standard deviation is 50. The sample mean was 200.
1. Estimate the population mean with 95% confidence.
2. Repeat part (a) changing the population standard deviation to 25.
3. Repeat part (a) changing the population standard deviation to 10.
4. Describe what happens to the confidence interval estimate when the standard deviation
is decreased.
A statistics practitioner took a random sample of 50 observations from a population whose
standard deviation is 25 and computed the sample mean to be 100.
a) Estimate the population mean with 90% confidence.
b) Repeat part (a) using a 95% confidence level.
c) Repeat part (a) using a 99% confidence level.
d) Describe the effect on the confidence interval estimate of increasing the confidence level.
Suppose that a random sample of five observations was taken from a normal population whose variance is 25. The results are 8, 15, 12, 6, 7. Find the 99% confidence interval estimate of the population mean.
The heights of children two years old are normally distributed with a mean of 80cm and a standard deviation of 3.6cm. Pediatricians regularly measure the heights of toddlers to determine whether there is a problem. There may be a problem when a child is in the top or bottom 5% of heights.
a) Determine the heights of two-year old children that could be a problem.
b) Fund the probability of these events
i. A two-year old child is taller than 90 cm
ii. A two-year old child is shorter than 85 cm
iii. A two-year old child is between 75 and 85 cm
Companies are interested in the demographic of those who listen to the radio programs they sponsor. A radio station has determined that only 20% of listeners phoning into a morning talkback program are male. During a particular week, 200 calls are received by this program.
a) What is the probability that at least 50 of these 200 callers are male?
b) What is the probability that more than half of these 200 callers are female?
c) There is a 30% chance that the number of male callers among the 200 total callers does not exceed what?
The maintenance department of a city’s electric power company finds that it is cost-effective to replace all street bulbs at once, rather than to replace the bulbs individually as they burn out. Assume that the lifetime of a bulb is normally distributed, with a mean of 3000 hours and a standard deviation of 200 hours.
a) If the department wants to more than 1% of the bulbs to burn out before they are replaced, after how many hours should all of the bulbs be replaced?
b) If two bulbs are selected at random from among those that have been replaced, what is the probability that at least one of them has burned out?
Let X be a normal random variable with a mean of 50 and a standard deviation of 8. Find the following probabilities:
a) P( X ≥ 52 )
b) P( X < 40 )
c) P(X =40 )
d) P( X > 40 )
e) P( 35 ≤ X ≤ 64 )
f) P( 32 ≤ X ≤ 37 )
Use Cumulative Standardized Normal Probability table to find the value z* for which:
a) P( Z ≤ z*) = 0.95
b) P( Z ≤ z*) = 0.2
c) P( Z ≤ z*) = 0.25
d) P( Z ≥ z*) = 0.9
e) P( 0 ≤ Z ≤ z*) = 0.41
f) P( -z* ≤ Z ≤ z*) = 0.88
Use Cumulative Standardized Normal Probability table to find the following probabilities
a) P( Z ≤ -1.96)
b) P( Z ≤ 2.43)
c) P( Z ≥ 1.7)
d) P( Z ≥ -0.95)
e) P( -2.97 ≤ Z ≤ -1.38)
f) P( -1.14 ≤ Z ≤ 1.55)
Use Cumulative Standardized Normal Probability table to find the area under the standard normal curve between the following values:
a) z=0 and z=2.3
b) z=0 and z=1.68
c) z=0.24 and z=0.33
d) z=-2.75 and z=0
e) z=-2.81 and z=-1.35
f) z=-1.73 and z=0.49
