Respuesta :
Answer:
The probability that a randomly selected bag of 200 candies has 50 or more green candies is P=0.04.
Step-by-step explanation:
We have a population with green candies proportion p=0.2.
If the bag comes with n=200 candies, then the mean green candies per bag is:
[tex]\mu=np=0.2*200=40[/tex]
The standard deviation is:
[tex]\sigma=\sqrt{np(1-p)}=\sqrt{200*0.2*0.8}=\sqrt{32}=5.66[/tex]
We have to calculate the probability that an individual bag has 50 green candies out of 200. We will then calculate the z-score:
[tex]z=(X-\mu)/\sigma=(50-40)/5.66=10/5.66=1.767[/tex]
The probability of having 50 or more green candies per bag is then:
[tex]P(X\geq50)=P(z>1.767)=0.04[/tex]
The probability that a randomly selected bag of this size has 50 or more green candies is 3.8%.
How to calculate probability?
The mean of the population will be:
= np
= 200 × 0.20
= 40
The standard deviation will be:
= ✓200 × ✓20(1 - 0.20)
= ✓32
= 5.6569
Therefore, the probability will be:
= 1 - P[(Z < (50-40)/5.6569
= 1 - P(Z < 1.77)
This under the normal table will be 3.8%.
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