A psychologist believes that 78% of male drivers when lost continue to drive, hoping to find the location they seek rather than ask directions. To examine this belief, he took a random sample of 48 male drivers and asked each what they did when lost. If the belief is true, determine the probability that less than 34 said they continue driving. Please use at least 3 decimal places in your z-score when finding the probability. Don't forget the continuity correction! Probability
A psychologist believes that 78% of male drivers when lost continue to drive, hoping to find the location they seek rather than ask directions. To examine this belief, he took a random sample of 48 male drivers and asked each what they did when lost. If the belief is true, determine the
Probability
78% of male drivers when lost continue to drive, hoping to find the location they seek rather than ask directions.
So, the probability that a male driver will continue to drive, p = 0.78
A sample of n = 48 male drivers were taken and interviewed.
Define the random variable,
X : Number of drivers chose to continue driving
X can be modeled as binomial distribution with parameters n = 48 and p = 0.78
Mean , E(X) = np = 37.44
Variance, Var(X) = np(1-p) = 8.2368
Now, X can be approximated by normal distribution with mean 37.44 and variance 8.2368
X ~ N(37.44,8.2368)
So,
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