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The intelligence quotients (IQs) of 16 students from one area of a city showed a mean of 107 and a standard deviation of 10, while the IQs of 14 students from another area of the city showed a mean of 112 and a standard deviation of 8. What would be the ‘ t ’ value to test whether there is a significant difference between the IQs of the two groups at significance level 0.01?
a. 2.56
b. 1.45
c. 3.45
d. 2.22
The weight of teenagers in Barangay Payapa approaches a normal distribution with a mean of 52.9 kg and a standard deviation of 7.2 kg. If a teenager is a chosen at random from Barangay Payapa, what is the probability that his/her weight is above 48.5 kg?
1. Consider the following contingency table analyzing the relationship between major and mathematics score.
Column Variables
Row Variables
(L)
(B)
(M)
Natural Sciences (N)
50
80
80
Social Sciences (S)
60
70
80
If there is a random selection of one student, determine the following probabilities:
a. P(N) b. P(B) c. P(N Ո L) d. P(M Ս S) e. P(B|N)
In testing a certain kind of truck tire over a rugged
terrain, it is found that 25% of the trucks fail to
complete the test run without a blowout. Of the next
15 trucks tested, find the probability that a) From 3
to 6 have blowouts; b) Fewer than 4 have blowouts;
C) More than 5 have blowouts.
If a given score is at the 30th percentile for reference group A and the same score is at the 60th percentile for reference group B, how do the two groups compare in terms of performance
An experiment has a binary outcome. Either success or failure. The probability of success is always 0.15. Suppose that the experiment is repeated 30 times.
a. Find out the probability that there are exactly 10 successes.
b. Calculate the same probability using a Normal Approximation. Is the approximation good? If so why? If not why not?
A supervisor at an electric bulb factory examines bulbs produced in the factory for defects. She usually finds that there are 14 defective bulbs in a week (7 days).
a. What is the probability that there are exactly 3 defective bulbs in one day?
b. What is the probability that there are less than 5 defects in a day?
c. Suppose the supervisor joins work, find the probability that 72 hours go by before she discovers her first defective bulb.
According to IT department of leading financial firm, 50% of emails received by their employees are spam. They are planning to install a software which filters the spam emails. A reputable cybersecurity brand has launched a software which claims to detect 99% of spam emails. However, they have also reported 5% as the chance of detecting a nonspam email as spam. If an email is detected as spam, what is the probability of it in fact being a non-spam email?
Rohini has 3 scarfs which are identical in shape, form and cloth material. They are only different in colours. The first scarf is coloured red on both sides while both the sides of second scarf are coloured black. The third scarf is coloured black on one side and red on the other. She mixes the 3 scarfs in a box and randomly selects one scarfs and puts it down on the ground. If the upper side of the selected scarf is red in colour, what is the probability of the other side of the scarf to be black?
JGU students recently conducted a study to record the height of Asian Females in Haryana. They found the heights to be normally distributed with a mean 66 inches and a standard deviation of 2.5 inches.
a. Suppose a female is randomly selected. What is the probability of her height being between 65 and 69 inches.
b. Is it possible to meet a female in Haryana with a height more than 72 inches?
