HW20 - Probability Distributions & Magali's Model - Science & Maths Assignment Help

Assignment Task

Q1. 

Magali is studying the mean total cloud cover, in oktas, for Leuchars in 1987 using data  from the large data set. The daily mean total cloud cover for all 184 days from the large  data set is summarised in the table below. 

One of the 184 days is selected at random. 

(a) Find the probability that it has a daily mean total cloud cover of 6 or greater. 

• Magali is investigating whether the daily mean total cloud cover can be modelled using a binomial  distribution. 
• She uses the random variable X to denote the daily mean total cloud cover and believes that X ~ B(8,  0.76) .

Using Magali's model, 

(b) (i) find P(X ≥ 6) 

(ii) find, to 1 decimal place, the expected number of days in a sample of 184 days  with a daily mean total cloud cover of 7 

(c) Explain whether or not your answers to part (b) support the use of Magali's model.

There were 28 days that had a daily mean total cloud cover of 8  For these 28 days the daily mean total cloud cover for the following day is shown in the  table below. 

(d) Find the proportion of these days when the daily mean total cloud cover was 6 or greater

Q2. Three bags, A, B and C, each contain 1 red marble and some green marbles. 

• Bag A contains 1 red marble and 9 green marbles only 
• Bag B contains 1 red marble and 4 green marbles only 
• Bag C contains 1 red marble and 2 green marbles only 
• Sasha selects at random one marble from bag A.  
• If he selects a red marble, he stops selecting.  
• If the marble is green, he continues by selecting at random one marble from bag B.  If he selects a red marble, he stops selecting.  
• If the marble is green, he continues by selecting at random one marble from bag C. 

(a) Draw a tree diagram to represent this information. 

(b) Find the probability that Sasha selects 3 green marbles. 

(c) Find the probability that Sasha selects at least 1 marble of each colour. 

(d) Given that Sasha selects a red marble, find the probability that he selects it from bag B.

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