Data Management

Stuck with 2 questions. Need of assistance before tomorrow.

Question 1. A summer camp has seven 4.6m canoes, ten 5.0m canoes, four 5.2m canoes, and four 6.1m canoes. Canoes are assigned randomly for campers going on a canoe trip.
a) Show the probability distribution for the length of an assigned canoe.
b) What is the expected length of an assigned canoe?

Question 2. A computer-chip manufacturer knows that 72% of the chips produced are defective. Suppose 3000 chips are produced every hour.
a)What is the probability that:
i)at At least 800 chips are acceptable?
ii)exactly 800 chips are acceptable?

b)For(ii), compare the results of using the binomial distribution with those found using the normal approximation.

For these questions I need to use either probability distribution, binomial distribution and or normal approximation of binomial distribution.

For 1, use the given probability distribution.

For 1a, I would use a simple bar chart. On the x-axis show the 4 boat sizes, on the y-axis show probability. The first bar would rise to a height of 7/25, the second to 10/25, and so on.

1b) (7/25)*4.6 + (10/25)*5.0 + (4/25)*5.2 + (4/25)*6.1

2) Ue the normal approximation to the binominal. Here, the standard deviation of the estimate is sqrt(n*p*(1-p)). So, the expected number of good chips is .28*3000=840, with a sd of sqrt(.28*.72*3000) = 24.6
So Z=(840-800)/24.6=1.63. Look up 1.63 in a cumulative normal distribution table (probably in your stats book). I get .9484. Meaning there is a 94.84% chance of seeing 800 or better acceptable

2b) Repeat the steps in 2a, except calculate the probability of getting 799 or better and subtract the probability of getting 800 or better (94.84%)

Now I understand. Thank you very much for your help!

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asked by Aurora

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