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You pay 168 dollars to play a lottery. A bin contains 91 balls labeled from 1 to 91. You draw a ball and you receive cash in the amount of 3 times the number shown on the ball. Let X be the number shown on the ball.
(a) Identify the probability distribution for the X.
Distribution = Parameter =
(b) Calculate the probability that you get more money back than you have spent on the ticket.
P(you win) =
(c) Calculate the average number that you will draw. Calculate the standard deviation for this number.
μ =
σ =
(d) Calculate the average amount that you will gain (winnings minus what you paid) by purchasing a ticket. Calculate the standard deviation associated to this number.
Average Gain (Winnings - paid) =
SD of Gain =
Using the new score formula, x = μ + (z)(σ), find the new standard scores of all the z-scores using the new mean of 115 and standard deviation of 10. Round off the new standard scores to whole numbers.
You have a coin that will flip heads with probability 0.38. You flip that coin 19 times. Let X be the number of heads in your 19 flips.
a) Identify the probability distribution for X.
Distribution =
First Parameter =
Second Parameter =
b) Compute the probability that exactly 9 heads will be flipped.
P(X = 9) =
c) Compute the mean and standard deviation associated with X.
μ =
σ =
The following simple random sample was selected from a normal distribution: 4, 6, 3, 5, 9, and 3.
a. Construct a 90% confidence interval for the population mean μ.
b. Construct a 95% confidence interval for the population mean μ.
c. Construct a 99% confidence interval for the population mean μ.
A student obtained a score of 45 in Math and a score of 60 in Science. If the mean and standard deviation of the math scores are 26.4 and 7.2, respectively, while that of science are 42.5 and 12.6,
The latest nationwide political poll indicates that for Indians who
are randomly selected, the probability that they are with alliance
ABC is 0.55, the probability that they are with alliance PQR is
0.30 and the probability that they are with alliance XYZ is 0.15.
Answer the following questions pertaining to a randomly chosen
group of 10 Indians.
What is the probabilities:
(i) None are with alliance ABC ?
(ii) 2 are with alliance XYZ ?
(iii) At least 8 are with alliance PQR ?
n a game of gambling a player tossesa fair coin. Ifit falls head,he wins 100 cedis and if it
falls tail he loss 100 cedis. Aplayer with 800 cedis tossesthe coin six times. What is the
probability that he will be left with 600 cedis?
A random sample of weight of 10 Ragi earheads (gm) : 40, 120, 100, 110, 112, 212, 115, 114, 118. Do the data support the assumed population mean weight of 100 gm? Find 95% confidence limits for the population (tα= 2.261).
Samples of size 25 are selected from a population with a mean of 40 and a standard deviation of 7.5. What is the mean of the sampling distribution of sample means?
In the mid-1990s, time magazine reported that 27% of the US Congress supported a tax cut as a means of stimulating the economy and increasing Tax revenues. Suppose at that time five members of congress were randomly selected for an interview and asked whether they supported the tax cut to stimulate the economy.
Find the probability that:
2.1 At least three of the five members were in favour of a tax cut. (6)
2.2 Less than five members were in favour of a tax cut. (6)
2.3 Not more than 3 members were in favour of the tax. (6)
2.4 Find the mean of the above distribution (6)
2.5 Find the variance and standard deviation of the above distribution (6)
