Statistics: Normal Distribution and Confidence Interval

The area under the curve to the left of the unknown quantity must be 0.7 (70%). So, we must first find the z value that cuts off an area of 0.7 in the left tail of standard normal distribution. Using the cumulative probability table, we see that z=0.53.

2. In order to determine the average amount spent in November on Amazon.com a random sample of 144 Amazon accounts were selected. The sample mean amount spent in November was $250 with a standard deviation of $25. Assuming that the population standard deviation is unknown, what is a 95% confidence interval for the population mean amount spent on Amazon.com in November?

(a) Then mean of the sample and the value of Z with an area of 10% in right tail.

9. Assume the weight, W, of a randomly selected adult has a normal distribution with a mean

Let’s assume you have taken 1000 samples of size 64 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 49.

Body weight expressed as a percentage of ideal in an SRS of n = 9 girls selected at random are as follows {114, 100, 104, 94, 114, 105, 103, 105, 96}. Calculate a 95% confidence interval for the population mean µ.

An intelligence test for which the scores are normally distributed has a mean of 100 and a standard deviation of 15. Use this information to describe how the scores are distributed.

Population A and Population B both have a mean height of 70.0 inches with an SD of 6.0. A random sample of 30 people is picked from population A, and random sample of 50 people is selected from Population B. Which sample mean will probably yield a more accurate estimate of its population mean? Why? Despite, both Population A and Population having a mean height of 70.0 inches with an SD of 6.0, Population B will

21. Suppose that you are designing an instrument panel for a large industrial machine. The machine requires the person using it to reach 2 feet from a particular position. The reach from this position for adult women is known to have a mean of 2.8 feet with a standard deviation of .5. The reach for adult men is known to have a mean of 3.1 feet with a standard deviation of .6. Both women’s and men’s reach from this position is normally distributed. If this design is implemented:

2. For the following set of scores, fill in the cells. The mean is 74.13 and the standard deviation is 9.98.

There are only 25 numbers in the sample collected. For purposes of analysis, it will be considered that the process itself is normally distributed, and its standard deviation is unknown. Under these conditions, the formula that gives the confidence interval is:

The customers in this case study have complained that the bottling company provides less than the advertised sixteen ounces of product. They need to determine if there is enough evidence to conclude the soda bottles do not contain sixteen ounces. The sample size of sodas is 30 and has a mean of 14.9. The standard deviation is found to be 0.55. With these calculations and a confidence level of 95%, the confidence interval would be 0.2. There is a 95% certainty that the true population mean falls within the range of 14.7 to 15.1.

Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of

A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at the .10 level of significance, that

28. The Polo Development Firm is building a shopping center. It has informed renters that their rental spaces will be ready for occupancy in 19 months.  If the expected time until the shopping center is completed is estimated to be 14 months, with a standard deviation of 4 months, what is the probability that the renters will not be able to occupy in 19 months?