Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper c
ar loader is set to put 84 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 84 tons and standard deviation σ = 0.7 ton. (a) What is the probability that one car chosen at random will have less than 83.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 29 cars chosen at random will have a mean load weight x of less than 83.5 tons of coal? (Round your answer to four decimal places.)
1 answer:
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Answer:
50.72 us fl oz
Step-by-step explanation:
Given:
500 ml of ingredient to be mixed with 1000 ml of another ingredient.
Now we need to convert ml into Ounces.
Formula:
Answer:
Step-by-step explanation:
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The t distribution or Student’s t-distribution is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".
The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.
Data given
Confidence =0.99 or 99%
represent the significance level
n =16 represent the sample size
We don't know the population deviation
Solution for the problem
For this case since we don't know the population deviation and our sample size is <30 we can't use the normal distribution. We neeed to use on this case the t distribution, first we need to calculate the degrees of freedom given by:
We know that so then
and we can find on the t distribution with 15 degrees of freedom a value that accumulates 0.005 of the area on the left tail. We can use the following excel code to find it:
"=T.INV(0.005;15)" and we got on this case since the distribution is symmetric we know that the other critical value is