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Percent of red lights last between 2.5 and 3.5 minutes is 95.44% .
<u>Step-by-step explanation:</u>
Step 1: Sketch the curve.
The probability that 2.5<X<3.5 is equal to the blue area under the curve.
Step 2:
Since μ=3 and σ=0.25 we have:
P ( 2.5 < X < 3.5 ) =P ( 2.5−3 < X−μ < 3.5−3 )
⇒ P ( (2.5−3)/0.25 < (X−μ)/σ < (3.5−3)/0.25)
Since, Z = (x−μ)/σ , (2.5−3)/0.25 = −2 and (3.5−3)/0.25 = 2 we have:
P ( 2.5<X<3.5 )=P ( −2<Z<2 )
Step 3: Use the standard normal table to conclude that:
P ( −2<Z<2 )=0.9544
Percent of red lights last between 2.5 and 3.5 minutes is % .
Answer:
P(X≤5)=0.5357
Step-by-step explanation:
Using the binomial model, the probability that x adults from the sample, are pessimistic about the future is calculated as:
Where n is the size of the sample and p is the probability that an adult is pessimistic about the future of marriage and family. So, replacing n by 20 and p by 0.27, we get:
Now, 25% of 20 people is equal to 5 people, so the probability that, in a sample of 20 American adults, 25% or fewer of the people are pessimistic about the future of marriage and family is equal to calculated the probability that in the sample of 20 adults, 5 people of fewer are pessimistic about the future of marriage and family.
Then, that probability is calculated as:
P(X≤5)= P(1) + P(2) + P(3) + P(4) + P(5)
Where:
Finally, P(X≤5) is equal to:
P(X≤5) = 0.0018+0.0137 + 0.0480 + 0.1065 + 0.1675 + 0.1982
P(X≤5) = 0.5357