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Standard Deviation and The Central Limit Theorem

1. Assume that blood pressure readings are normally distributed with a mean of 117 and a standard deviation of a = 6.4.

If one person is randomly selected, find the probability that their blood pressure will be less than 119.

If 64 people are randomly selected, find the probability that their mean blood pressure will be less than 119. Use the Central Limit Theorem.

Which of the two situations is more likely to happen?

2. The average teacher's salary in North Dakota is u= $29863 . Assume a normal distribution with a = $5100.

If one teacher is randomly selected, find the probability that their salary will be greater than $40,000.

If 80 teachers are randomly selected, find the probability that their mean salary will be greater than $30,000. Use the Central Limit Theorem.

Solution Preview

1.
a. Let x be the random variable having normal with mean 117 and standard deviation 6.4

P(X<119)= ?

We have

Z = (X-117)/6.4

Z = (119-117)/6.4

Z = 0.3125

P(Z<0.3125) = 0.5 + 0.1217

= 0.6217

b. n= ...

Solution Summary

This solution calculates probability using the central limits theorem.

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