Question

the following questions are either true or false answers

1. The Central Limit Theorem allows one to use the Normal Distribution for both normally and non-normally distributed populations.

2. A random sample of 25 observations yields a mean of 106 and a standard deviation of 12. Find the probability that the sample mean exceeds 110. The probability of exceeding 110 is 0.9525.

3. Suppose the average time spent driving for drivers age 20-to-24 is 25 minutes and you randomly select 50 drivers. What is the probability that the mean time they spend driving each day is between 24.7 and 25.5 minutes, assuming that the standard deviation is 1.5 minutes?

P(24.7<X<25.5) =0.9116

4. An electrical firm manufactures a certain type of light bulb that has a mean life of 1,800 hours and a standard

deviation of 200 hours. Find the probability that a random sample of 100 bulbs will have an average life of more than 1,825 hours.

P(X>1,825) =0.1056

5. A manufacturing company receives a shipment of ball bearings each month from a supplier. The inspector applies the following rule in deciding whether or not to accept or reject each shipment: If the mean diameter of the sample is between 0.245 and 0.255 the shipment is accepted otherwise the shipment is rejected. A random sample of 36 bearings is selected and measured. What is the probability of accepting the shipment that has a mean diameter of 0.240 inches and a standard deviation of 0.015 inches? The probability of accepting the shipment is 0.0228.

6. According to the M&M website, the average percentage of brown M&M candies in a package of milk chocolate M&Ms is 13%. Suppose you randomly select a package of milk chocolate M&Ms that contains 55 candies and determine the proportion of brown candies in the package. What is the probability that the sample

percentage of brown M&M candies is less than 20%?

P(p<0.20)=0.9382

7. The average income of a business analyst is $68,936 as reported by the US Bureau of Labor Statistics. A sample of 81 business analysts yield a standard deviation of $10,000. The probability of an annual income of a business analyst is between $67,000 and $70,000 is 0.8289.

8. The mean weight of 2000 male subjects whose height ranges between 5 feet 11 inches to 6 feet is 183 pounds with a standard deviation of 6 lbs. The probability that in a sample of 44 male subjects whose weight exceeds 185 pounds is 0.136.

9. According to the National Center for Health Statistics 15% of all Americans have hearing impediments. In a random sample of 120 Americans, the probability that less than 12% have hearing impediments is 0.1788.

10. The probability that a person in the LA area who has at least a baccalaureate degree is 0.21. From a group of 400 persons randomly selected from LA the probability that the proportion ranging from 17% to 24% of persons having a baccalaureate degree is 0.9104.

Answer 1

1)

True

2)

This is a normal distribution question with

Sample size (n) = 25

Since we know that

P(x > 110.0)=?

The z-score at x = 110.0 is,

z = 1.6667

This implies that

P(x > 110.0) = P(z > 1.6667) = 1 - 0.9522129635397043

False

PS: you have to refer z score table to find the final probabilities.
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