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Statistics, EXT1 S1 2024 MET1 4

Let be a binomial random variable where  .

  1. Find the standard deviation of .   (1 mark)

  2. Find  .   (2 marks)

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a.   

b.   

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a.    
   
   
   

 

b.    
   
   
   
Mean mark (b) 51%.

Statistics, EXT1 S1 2020 HSC 12b

When a particular biased coin is tossed, the probability of obtaining a head is .

This coin is tossed 100 times.

Let be the random variable representing the number of heads obtained. This random variable will have a binomial distribution.

  1. Find the expected value, .  (1 mark)

  2. By finding the variance, , show that the standard deviation of is approximately 5.  (1 mark)

  3. By using a normal approximation, find the approximate probability that is between 55 and 65.  (1 mark)

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i.   

 
 

 

ii.   
   
   

 

 

 

iii.   
   

Statistics, EXT1 S1 EQ-Bank 10

Four cards are placed face down on a table. The cards are made up of a Jack, Queen, King and Ace.

A gambler bets that she will choose the Queen in a random pick of one of the cards.

If this process is repeated 7 times, express the gambler's success as a Bernoulli random variable and calculate

  1. the mean.  (1 mark)

  2. the variance.  (1 mark)

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i.     

 
 

 

ii.  
   
   

Statistics, EXT1 S1 SM-Bank 4

In an experiment, a pair of dice are rolled 70 times.

A success is recorded if the sum of the dice roll is 5 or less.

  1. What is the mean of this binomial distribution?

     

    Give your answer to one decimal place.  (3 marks)

  2. What is the standard deviation?

     

    Give your answer to one decimal place.  (1 mark)

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i.   

STRATEGY: A table (or array) can be a very efficient and error minimising strategy in questions like this.

 
 

 

ii.