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A Mathematics professor is teaching both a morning and an afternoon section of introductory calculus. Let A={the professor gives a bad morning lecture} and B={the professor gives a bad afternoon lecture}. If P(A) = 0.3, P(B) = 0.2 and P(A ∩ B) = 0.1. Calculate the following probabilities:
(a) P(B|A)
(b) P(B'|A)
(c) P(B|A' )
(d) P(B'|A')
(e) If at the conclusion of the afternoon class, the professor is heard to mutter “what a rotten lecture", what is the probability that the morning lecture was also bad?
It has been determined that
the probability that the first inspector will miss a defective item is 0.09. If a defective
item gets past the first inspector, the probability that the second inspector will not detect
it is 0.01. What is the probability that a defective item will not be rejected by either
inspector
All products on an assembly line must pass two inspections. It has been determined that
the probability that the first inspector will miss a defective item is 0.09.
An XYZ business can currently produce 251 per hour of 5 amp fuses. The supplier claims that a new machine has been purchased and installed that will boost the manufacturing rate. The mean hourly production on the new machine was 259, with a sample standard deviation of 6 per hour, according to a sample of ten hours randomly selected from last month.
The head supervisor of three discount pharmacy stores wants to know how many discount coupons are redeemed in his stores. The findings of the survey are listed in the table below. At α=0.01
α=0.01, test the hypothesis that redemption level and location are related.
Store LocationRedemption LevelMidtownNorthsideSouthsideHigh5010660Medium
899579Low241170
The head supervisor of three discount pharmacy stores wants to know how many discount coupons are redeemed in his stores. The findings of the survey are listed in the table below. At α=0.01
α=0.01, test the hypothesis that redemption level and location are related.
Store LocationRedemption LevelMidtownNorthsideSouthsideHigh5010660Medium
899579Low241170
In the past, the average age of employees of a large corporation is more than 27 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees, a sample of 36 employees was selected. The average age in the sample was 30 years with a population standard deviation of 8 years. Use the 5% signification level to test the claim. (20marks)
1. The distance traveled per taxi per year is normally distributed with a mean of 40 thousand miles and a variance of 169 thousand miles. Compute the probability of taxi can be expected to travel:
a. between 30 and 70 thousand miles in a year.
[4 marks]
b. above 60 thousand miles in a year.(3 marks)
c. above 27 thousand miles in a year.
[3 marks]
The head supervisor of three discount pharmacy stores wants to know how many discount coupons are redeemed in his stores. The findings of the survey are listed in the table below. At α=0.01
α=0.01, test the hypothesis that redemption level and location are related.
In a particular city, one in three families have a phone in their home. If 90 families are chosen at random, calculate the probability that at least 30 of them will have a phone.
