Statistics and Probability Answers

In a game 2 red balls & 8 blue balls are placed in a bottle. The bottle is shaken & Mary draws 3 balls at random & w/o replacement. The number of red balls that she draws is denoted by R. Mary scores 4 points for each red ball that she draws. The balls are now replaced in a bottle and the bottle is shaken again. John draws 3 balls at random & w/o replacement. He scores 1 point for each blue ball that he draws. Mary's score is denoted by M & John's score is denoted by J. Find the expectation & variance of M-J. Expectation of R is 3/5 & variance is 28/75 Ans: 0, 476/75

A three digit number with no digit of repeted is made from the digit 3 to 8.What is the probability that the numnber is ;
1.odd?
2.even?
3.between 200 and 500?
4.a multiple by 5
5.between 500 and 700?

Generally a new program may have the following types of errors: LOGIC error (L),
RUNTIME error (R) and SYNTAX error (S). The testing on the 80 new programs revealed;
18 programs had no errors; 5 programs had all three types errors; 14 programs had only
LOGIC errors; 6 programs had only RUNTIME errors; 17 programs had both SYNTAX and
RUNTIME errors; 12 programs had both SYNTAX and LOGIC errors.

a) Use a Venn diagram to illustrate the above problem including the given
numerical values. In your diagram, label with x and y the two region which
cannot be enumerated.

b) If the number of programs had SYNTAX error is the same as the number of
programs had LOGIC errors, derive a pair of simultaneous equations in terms
of x and y .

c) Solve the equations in b).

A new Firestone tire is guaranteed to last for 40,000 miles. The actual mean life of the tires is 47,000 miles with a standard deviation of 4,000 miles.

a) What percent of the tires will last for at least 40,000 miles?
b) What percent of the tires will not last for at least 40,000 miles?
c) What is the probability that a tire will last for more than 50,000 miles?
d) The Firestone Company wants to advertise how long some of their tires last. They decide to state how long the top 3% of their tires will last. How many miles will the top 3% of their tires last?

What are the independent and dependent variables in this hypothesis: treatment with Bosentan will increase a patient's ability to walk without fatigue?

When we can use t-statistics instead of z-statistics?

What is happening with normal distribution when the value of standard deviation increases?

What is the probability of being born on:
a)the 10th of a month in a non-leap year.
b)Christmas day in non-leap year.
c)the 29th February.

How the sample standard deviation and the sample variance are related?

What is the finite population correction factor?