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Let X1, X2,….., Xn be independently and identically distributed b(1, p) random variables. Obtain a confidence internal for p using Chebychev’s inequality.
The scores of high school students on a national mathematics exam in SA were normally distributed with a mean of 86 and a standard deviation of 4. If there were 97680 students with scores higher than 91. how many students took the test? 394400 125000 247667 No correct answer provided 925000 105000
The null hypothesis regarding a contingency table with 6 rows and 4 columns should be rejected (at 95% confidence) if the test statistic is greater than
The calculated value of chi- square (10.14) with 4 degree of freedom at 1% level of significance level.
The p-value is p=0.0381can I know how to find the p value ?
A courier service company has found that their delivery time of parcels to clients is approximately normally distributed with a mean delivery time of 30 minutes and a variance of 25 minutes (squared). Required: a) What is the probability that a randomly selected parcel will take more than 26 minutes to deliver? (2) b) What is the minimum delivery time (minutes) for the 2.5% of parcels with the longest time to deliver? (4
A LED company claims that the average life of the LED light bulbs it
manufactures is 1, 500 hours with a standard deviation of 500 hours. If a random sample of 40 bulbs is chosen, what is the probability that the sample mean will be:
a. greater than 1, 400 hours?
b. less than 1, 400 hours?
An insurance company found that 25% of all insurance policies are terminated before their maturity date. Assume that 15 polices are randomly selected from the company’s policy database. Required: Out of the 15 randomly selected policies; a) What is the expected number of policies to be terminated before maturing? (2) b) What is the probability that no policy will be terminated before maturity? (2) c) What is the probability that all policies will be terminated before maturing? (2) d) What is the probability that at least two policies will be terminated? (4) e) What is the probability that more than 8 but less than 11 policies will be terminated? (5) f) What is the probability that eight policies will not be terminated? (3) g) What is the probability that 18 policies will be terminated?
Two coins are tossed. If A is the event “head on the first coin”, B is the event “head on the second coin” and C is the event “coins fall alike”, show that the events A, B, and C are pair wise independent but not completely independent.
10000 ‘Roshani’ light bulbs with a mean life of 150 days are installed in a new factory and their length of life is normally distributed with standard deviation of 10 days. How many Roshani-bulbs will expire in less than 160 days?
Suppose the joint p.d.f of (X,Y) is given by f(x,y) = x^2 + xy/3 0 < x < 1 , 0 < y < 2 = 0 otherwise a) Verify that given f(x,y) is a joint density function? b) Find marginal and conditional probability density functions? c) Compute P (Y < ½ | X < ½ )
