Question
Asked Feb 18, 2019
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From experience you know that 83% of the desks in the schools have gum stuck
beneath them. In a random sample of 14 desks.
a) Compute the probability that all of them have gum underneath.
b) Compute the probability that 10 or less desks have gum.
c) What is the probability that more than 10 have gum?
d) What is the expected number of desks in the sample have gum?
e) What is the SD of the number of desks with gum?

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Expert Answer

Step 1

Hello there! I see that there are multiple subparts in this question. I can answer only three sub parts of the question according to our policies. Please do find the solutions of first 3 subparts.

Percentage of desks in school have  gum stuck beneath them = 83%

Total number of desks = 14 = n

Proportion of desks in school which have gum stuck beneath them = 0.83 = p.

The binomial probability distribution function with total trials n and probability of success p is given by following formula

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Step 2

To compute probability that all of the desks with gum

So probability of success =probability of desk having gum beneath =p  = 0.83

total number of desk = 14

Here we need gums on all desk. So x =14 we need to find the probability that all of them have gum stuck beneath desk = 0.073636

 

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Step 3

We need to compute probability that 10 or less desks have gum.

P(X ≤ 10) here X be desks with gum beneath

P(X ≤10) = P(X=0) + P(X=1)+P(X=2)+...+P(X=10). Probability that desks with gum underneath less than equal to 10 in nothing but 1- P(X > 10)

P(X ≤ 10) = 1 - P(X=11)-P(X=12...

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