Statistics and Probability Answers

a) How many ways can a teacher form a committee of 3 members from a class of 4 boys and 3 girls?

b)How many committees in (a) has exactly one girl?

c)How many committees in (a) has at least one girl?

A population consists of N=7 numbers 1, 2, 2, 3, 4, 5, and XX. Draw all possible samples 

of size n=3 without replacement from this population and find the sample proportion of 

odd numbers in the samples. Construct the sampling distribution of sample proportion 

and verify 𝜇𝑝̂ = 𝑃 and 𝜎

2

𝑝̂ =

𝑝𝑞

𝑛

.

𝑁−𝑛

𝑁−1

where 𝑞 = 1 − 𝑝

Anxiety disorder

a) How many different ways can be letters in each of the following words be arranged?

i)YAHOO

ii)GOOGLE

b)How many of the arrangements in (a) will have the letters ‘O ́together?

construct all random samples consisting 2 observation from the given data you are asked to guess the average weight of 6th watermelons by taking a random sample without replacement from the population

a) Freddie has 6 toys cars and 3 toy buses, all different.

i)He chooses 4 toys to take on holiday with him. In how many different ways can Freddie choose 4 toys?

ii)Freddie arranges these 9 toys in a line. Find the number of possible arrangements

•if the buses are all next to each other.

•if there is a car at each end of the line and no buses are next to each other.

b) There are 2 purple cubes, 3 blue cubes, 2 red cubes, 4 orange cubes, 2 green cubes and 2 yellow cubes. Calculate the number of possible arrangements when all the cubes are arranged in a circle.

A fair six-sided die is tossed twice. What is the probability that a five will occur at least once?

An oil company is bidding for the rights to drill a well in field A and a well in field B. The probability it will drill a well in field A is 40%. If it does, the probability the well will be successful is 45%. The probability it will drill a well in field B is 30%. If it does, the probability the well will be successful is 55%. Calculate each of the following probabilities: 

a) probability of a successful well in field A, 

b) probability of a successful well in field B, 

c) probability of both a successful well in field A and a successful well in field B, 

d) probability of at least one successful well in the two fields together,

e) probability of no successful well in field A, 

f) probability of no successful well in field B, 

g) probability of no successful well in the two fields together (calculate by two methods), 

h) probability of exactly one successful well in the two fields together. Show a check involving the probability calculated in part h

Four of the light bulbs in a box of ten bulbs are burnt out or otherwise defective. If two bulbs are selected at random without replacement and tested, (i) what is the probability that exactly one defective bulb is found? (ii) What is the probability that exactly two defective bulbs are found?

A pilot plant has produced metallurgical batches which are summarized as follows: Low strength High... 1 answer below »

A pilot plant has produced metallurgical batches which are summarized as follows:

Low strength

High strength

Low in impurities

2

27

High in impurities

12

4

If these results are representative of full-scale production, find estimated probabilities that a production batch will be:

i) low in impurities

ii) high strength

iii) both high in impurities and high strength

iv) both high in impurities and low strength​