Statistics and Probability Answers

Five unbiased dice were thrown 96 times and the number of times 4, 5 or 6 was 

obtained, is given in the following table:

No. of dice  0. 1. 2. 3. 4. 5.

showing 4, 

5 or 6 

Frequency 1 10 24 35 18 8

At 5% level of significance test whether this data comes from a binomial distribution. 

You may like to use the following values. 

 [( x₅²10.05)=11.07 , x₆²(0.05)=12.59 ,x₇²(0.05)=14.07.]⁽

The yield (in kg) of 100 plots in the form of grouped frequency distribution is given 

below:

Yield(in kg) Frequency

0-20 6 

20-40 21 

40-60 35 

60-80 30 

80-100 8 

(i) Estimate the number of plots with an yield of 

(A)40 to 80 kg 

(B) 10 to 70 kg 

 (ii) Find the mean and standard deviation of yield.

For the given bivariate probability distribution of X and Y :

P(X=x , Y=y)=(x²+y)/32 for x=0,1,2,3 and y=0,1.

 Find: 

 (i) P(X ≤ 1 , Y =1)

 (ii) P(X ≤ 1)

 (iii) P(Y > 0) and 

 (iv) P(Y = 1 | X = 3)

Suppose X is a gamma variate with E(x) = 3 and var(X ) = .7 Find the parameters 

α and λ of the gamma distribution.

The probability density function of a random variable X is f (x) = C | x |; Find C,

and the value of x_o such that ,

F_X(x_o)=3/4 where F is the CDF.

If the moment generating function (m.g.f.) of a random variable X is 

M_x(t)=exp(3t+32t²).Find mean and standard derivation of X and also compute 

P(X<3).

In my original data pool I had 600 samples and I calculated pricing info and average distribution for those clusters.

I now have a lot more sample points and I am looking too add another 600 samples onto my original 600.

How would I go about selecting the second 600 in a way that does not disrupt my distribution rations between the clusters and the pricing info?

Also, how would I test for similarity between both sample sets?

Thanks!

A normal distribution has u=80 o=10. What is the probability of random selecting the following scores ?

a) x>75

b) x<85

c)between the mean of score of 90

d) between the mean of score of 50

e) 75< x >85

If a cup of ice cream is selected,what is the probability that the cholesterol content will be more than 670 mg?

Read and analyze the given problem. Provide a complete solution, Table, and a graph corresponds to the answer.

Due to ASF issue it was aired that the average price of a kilo of pork in MM is P195.00. However, a sample of 15 prices randomly collected from different markets in MM showed an average of P200.00 and with standard deviation of P9.50. using 0.05 significant level. What would be your conclusion for the price of pork in MM.