Question

In: Math

QUESTION FIVE The diameter of shafts produced in a machine follows a normal distribution with the...

QUESTION FIVE

  1. The diameter of shafts produced in a machine follows a normal distribution with the variance of 81mm. A random sample of 36 shafts taken from the production has its mean diameter of 30mm. Find a 95% confidence interval for the diameter of shafts.

  1. The Marketing manager of a company feels that 42% of retailers will have enhanced weekly sales after introducing an advertisement at the point of sales. A sample of 36 retailers shops of the company, where the point of sales advertisement has been displayed, reveals that only 18 of them are having enhanced sales after displaying the advertisement. Find the 95% confidence interval for the proportion representing the enhanced sales.

c. The Finance manager of a company feels that 55% of branches will have enhanced yearly collection of deposits after introducing a hike in interest rate. Determine the sample size such that the mean proportion is with plus or minus 0.05 confidence level of 90%?     

Solutions

Expert Solution



Related Solutions

The diameter of a cylinder follows a normal distribution with the mean of 10cm and the...
The diameter of a cylinder follows a normal distribution with the mean of 10cm and the variance of 0.04 cm^2. a) Construct a Shewhart chart to monitor the process mean of cylinder diameter with a sample size 9? (Use L=3) b) If the mean of the process changes to 10.5 cm, what is the probability that you detect this mean shift at the immediate next sample (the first sample after the mean shift)? c) Continue b), what is the probability...
The diameters of steel shafts produced by a certain manufacturing process should have a mean diameter...
The diameters of steel shafts produced by a certain manufacturing process should have a mean diameter of 0.255 inches. The diameter is known to have a standard deviation of 0.0001 inch. A random sample of 10 shafts was performed and the average diameter was 0.2545 inch. a. Set up appropriate hypotheses on the mean b. Test these hypotheses using α = 0.05 and α = 0.1. What are your conclusions? c. Find the P-value for this test. d. Construct a...
The diameters of steel shafts produced by a certain manufacturing process should have a mean diameter...
The diameters of steel shafts produced by a certain manufacturing process should have a mean diameter of 5.5 inches. The diameter is known to have a standard deviation of 0.9 inches. A random sample of 30 shafts. (a) Find a 90% confidence interval for the mean diameter to process. (b) Find a 99% confidence interval for the mean diameter to process. (c) How does the increasing and decreasing of the significance level affect the confidence interval? Why? Please explain and...
The diameters of steel shafts produced by a certain manufacturing process should have a mean diameter...
The diameters of steel shafts produced by a certain manufacturing process should have a mean diameter of 0.218 inches. The diameter is known to have a standard deviation of = 0.0003 inch. A random sample of 40 shafts has an average diameter of 0.2455 inches. a/ Test these hypotheses using α= 0.02, α= 0.05, and α= 0.09 b/ Comparing the data above. Does the results of your hypothesis testing change when you changed α? Explain. Please show your work and...
The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal...
The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 7.7 ounces and standard deviation 0.15 ounces. (a) What is the probability that the average weight of a bar in a Simple Random Sample (SRS) with four of these chocolate bars is between 7.59 and 7.86 ounces? (b) For a SRS of four of these chocolate bars, c) what is the level L such that there is a 3% chance that the...
The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal...
The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 7.8 ounces and standard deviation 0.2 ounces. (a) What is the probability that the average weight of a bar in a random sample with three of these chocolate bars is between 7.64 and 7.96 ounces? ANSWER: (b) For a random sample of three of these chocolate bars, what is the level L such that there is a 4% chance that the average...
The distribution of ages of all the employees in Company X follows a normal distribution. The...
The distribution of ages of all the employees in Company X follows a normal distribution. The average age is 40 and the standard deviation is 5. Find the Z-score of a 50 year old employee. What is the probability that a randomly chosen employee will be younger than 35 years? What is the probability that a randomly chosen employee will have an age between 35 and 45 years? What is the probability that a randomly chosen employee will be older...
The diameter of alloy rods produced on an extrusion machine are known to have a standard...
The diameter of alloy rods produced on an extrusion machine are known to have a standard deviation of 0.0001 inches. A random sample of 25 rods have a mean diameter of 0.5046 inches. a) Test the hypothesis that the mean diameter is 0.5025 inches. Assume a 2-sided alternative and use α=.05. Be sure to identify the decision rule, the critical values. Draw pictures to visualize. b) Construct the 2-sided 95% confidence interval for this test with α=.05. c) What is...
The process that produces a machined part has a normal distribution with the average diameter of...
The process that produces a machined part has a normal distribution with the average diameter of 7.2 cm and a standard deviation of 0.35 cm. What is the probability that a part will have a diameter between 7.1 cm and 7.6 cm? Select one: a. 0.4859 b. 0.8734 c. 0.3875 d. 0.2609
Assume the distribution of home selling prices follows a normal distribution. for this area the mean...
Assume the distribution of home selling prices follows a normal distribution. for this area the mean selling price is $95,140 and the standard deviation of the selling price is $13,100. Let S be the home selling price. For a randomly selected home find P(S>$100,000). The answer is approx. = .6447. I just really need to know how to set this question up in a TI-84 calculator PLEASE! It's urgent!
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT