Probability:Retail pack weights of Pencils are normally distributed with a mean of 98.6 grams and standard deviation of 0.73. Find the probability that a sample of 36 such retail packs have an average...

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Probability:Retail pack weights of Pencils are normally distributed with a mean of 98.6 grams and standard deviation of 0.73. Find the probability that a sample of 36 such retail packs have an average weight less than 98.3.
Confidence Interval :A sample of 200 pencils of certain variety shows that their average length is 15.7 mm. If the margin of error is 2.2mm @ 95% Confidence, construct the confidence interval.
Chi-square:A pencil factory is testing the variance in the mass of pencils produced. Sampling 15 pencils randomly shows variance of 3.4 grams. What is a 95% confidence interval for variance of all pencils produced.
Small samples-Normal Distribution:Pencil production supervisors believe they produce on average atleast 8 pallets per day. Management claims that they don't produce that many pallets consistently. Pallets are wooden base used for stacking many cartons and then they shrink wrap to ship the products using trucks to warehouses. They sample 19 production supervisor's lines who report a sample mean of 7.5 pallets produced per day with standard deviation of 1.1 pallets. Test Management's claim at 0.025 level of significance.
Large samples-Normal Distribution:Records show that a particular machine produces on average less than or equal to 850 pencils of certain variety on a given day. A maintenance company claims that they can overhaul the machine to produce on average higher than this. To test the maintenance company samples 1000 machines they overhauled which produced an average of 856 pencils with a standard deviaiton of 98 pencils after overhauling. At 0.05 level of significance, test the maintenance company claim.
P Values:A new graphite for pencils claims to lower the weight of each pencil by 20 points without lowering the quality. Batch A of 55 pencils were chosen and used the above graphite and lowered the weight by average of 44.7 points with standard deviation of 6.8 points.Batch B of 55 different set of pencils which did not use the above graphite lowered the weight by average 23.1 points with standard deviation of 5.3 points. Test the claim at 0.01 level of significance.
Hypothesis Testing:A new tool made a particular production line to produce more than 12 pencils as defective. To test , 15 days of data were taken and were analyzed . State H0 and Ha hypothesis.
Two Variences:A study claims that the variance in quantity produced in a non-overhauled machine is different than the overhauled machines.The sample variance in 5 non-overhauled machines is 545. The sample variance in 5 overhauled machines is 103. Test the claim at 0.01 level of significance (or 99% CI)
Answered 1 days AfterMay 02, 2021

Solution

Suraj answered on May 03 2021
23 Votes

Probability:
Retail pack weights of Pencils are normally distributed with a mean of 98.6 grams and standard deviation of 0.73.
The probability that a sample of 36 such retail packs have an...

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