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5) A study found that consumers spend an average of $24 per week in cash without...

5)

  • A study found that consumers spend an average of $24 per week in cash without being aware of where it goes.
  • Assume that the amount of cash spent without being aware of where it goes is normally distributed and that the standard deviation is $6.

What is the probability that a randomly selected person will spend more than $28?

Math   Statistics-And-Probability   
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Answer #1

Solution :

Let X be a random variable which represents the amount of cash spent without being aware of where it goes.

Given that, X ~ N(24, 6²)

μ = $24 and  σ = $6

We have to find P(X > $28).

We know that if X ~ N(μ, σ²) then,

Using "pnorm" function of R we get, P(Z > 0.67) = 0.2514

Hence, the probability that a randomly selected person will spend more than $28 is 0.2514.

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