SOLUTION: Psychologists estimate that 80% of male drivers, when lost in trying to find a location, continue to drive rather than asking for directions. If this estimate is correct, what is t

Question 750493: Psychologists estimate that 80% of male drivers, when lost in trying to find a location, continue to drive rather than asking for directions. If this estimate is correct, what is the probability that, in a random sample of 100 lost male drivers, the proportion who continue to drive is
a) at least 0.70?
b) less than 0.85?
please provide all step. I'm having a hard time understanding it. thank you
Found 2 solutions by reviewermath, stanbon:
Answer by reviewermath(1029) (Show Source): You can put this solution on YOUR website!
X ~ Binomial(100, 0.8)
a. P(X ≥ 70) = =
b. P(X < 85) = =
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Psychologists estimate that 80% of male drivers, when lost in trying to find a location, continue to drive rather than asking for directions. If this estimate is correct, what is the probability that, in a random sample of 100 lost male drivers, the proportion who continue to drive is
a) at least 0.70?
z(0.7) = (0.7-0.8)/sqrt[0.8*0.2/199] = -2.5
P(p-hat >= 0.7) = P(z >= -2.5) = normalcdf(-2.5,100) = 0.9938
==========================
b) less than 0.85?
z(0.85) = (0.85-0.8)/sqrt(0.8*0.2/100) = 1.25
----
P(p-hat <= 0.85) = P(z <= 1.25) = 0.8944
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Cheers,
Stan H.
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