1. Assume that blood pressure readings are normally distributed with a meanof 117 and a standard deviationof a = 6.4.

If one person is randomly selected, find the probabilitythat 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 distributionwith 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.

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= …

This solution calculates probability using the central limits theorem.