Search & Filtering
1. (i) Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for finding out:
(a) P(X>10); (b) P(X<18) (c) P(X>21) (d) P(9<X<14)
In a normal distribution 10% of the items are under 50 and 90% of the items are the under 80.find the values mean and standard deviation of the distribution?
find the value of Z such that
i. the area of the right of Z is 0.2266
ii. the area between -Z and Z is 0.5722
1. The average cholesterol content of a
certain canned goods is 215 milligrams
and the standard deviation is 15
milligrams. Assume the variable is
normally distributed.
a) If a canned good is selected, what is
the probability that the cholesterol
content will be greater 220
milligrams?
b) If a sample of 25 canned goods is
selected, what is the probability that
the mean of the sample will be
larger than 220 milligrams?
2. The number of driving miles before a
certain kind of tire begins to show wear
is on the average, 16,800 miles with a
standard deviation of 3,300 miles. A
car rental agency buys 36 of these tires
for replacement purposes and puts
each one on a different car.
a) What is the probability that the 36
tires will average less than 16,000
miles until they begin to show
wear?
b.What is the probability that the 36
tiles will average more than 18,000
miles until they begin to show
wear?
II – PROBLEM SOLVING:(week 7)
1. The average public high school has 468
students with a standard deviation of
87.
a) If a public school is selected, what
is the probability that the number of
students enrolled is greater than
400?
b) If a random sample of 38 public
elementary schools is selected, what
is the probability that the number of
students enrolled is between 445
and 485?
2. A certain population has a mean of 15.4
and a standard deviation of 5.6. If random
samples of size 5 is taken from this
population, which of the following statements
is correct?
a. The mean of the sampling distribution of
the sample means is equal to 15.4.
b. The mean of the sampling distribution of
the sample means is less than 15.4.
c. The standard deviation of the sampling
distribution of the sample means is 15.4.
d. The standard deviation of the sampling
distribution of the sample means 5.6.
3. How many possible of size n = 3 can be
drawn from a population of size 12?
a. 36 c. 144
b. 1728 d. 220
4.Taken from the same population, which
sample size will give a smaller standard error
of the mean?
a. 35 c. 18
b. 12 d. 9
6. What is the finite population correction
factor if the size of the population is 200 and
the sample size is 25?
a. 0.979 c. 0.938
b. 0.879 d. 0.856
8. If a population has a mean of 23.7, what is
the mean of the sampling distribution?
a. less than 23.7
b. larger than 23.7
c. closer to 23.7
d. the same as 23.7
9. If 50 randomly selected college students
take the examination, what is the probability
that the mean time it takes the group to
complete the test will be less than 43
minutes?
a. 23% c. 4.24%
b. 0.23% d. 0.42%
10. Please refer to item 9.
Does it seem reasonable that a college
student would finish the examination in less
than 43 minutes?
a. YES b. NO
A. Use the z-table to find the area that corresponds to each of the following:
1. z = 0.67
2. z = − 1.5
3. z = .78
4. z = − 2.35
5. z = 1.8
B. Given = 62 and = 8. Find the z-score value that corresponds to each of the following scores.
1. X = 50
2. X = 78
3. X = 82
Find the raw score that corresponds to each of the following.
4. = 8, = 52, z = − 1.5
5. = 15, = 75, z = 0.47
C. Solving Problem.
1. The length of human pregnancies from conception to birth approximates a normal
distribution with a mean of 266 days and a standard deviation of 16 days. What
probability/proportion of all pregnancies will last between 240 and 270 days (roughly
between 8 and 9 months)?
2. The result of a nationwide aptitude test in mathematics are normally distributed with = 80
and = 15.
a. What is the percentile rank of a score of 87?
b. What is the score that corresponds to a percentile rank of 94.5%?
Find the class boundaries midpoint and width for the class 47-55
The Coronavirus Disease is an infectious disease caused by a new strain of coronavirus. The World Health Organization claims that the incubation period of the virus in the infected person has a mean of 6.1 days. The doctors in the Philippines conducted a research and they found out that incubation period of the virus in human body is 7.03 days with a standard deviation of 4.32. The samples were 46 COVID patients. Is there enough evidence to conclude that the incubation period of the virus is 6.1 days as stated, at a=0.01?
