Math Questions Help

[D.D.S.]

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Hey guys I have a few math questions that I need help with so help me out if you can...

#1. The Army discovered that a recent shipment of grenades (both live and practice) had some labels inadvertently misapplied as to which case contained each kind. The manufacturer assured them that only 3% of the cases were labeled wrong. In a sample of 8 cases, what is the probability (show by calculation):
a) that no cases were labeled wrong
b) that no more that 1 case is labeled incorrectly.

#2. Shampoo is sold in bottles that are labeled 16.00 ounces although they could hold up to 16.24 oz. A study of the filling process shows normal distribution [i.e. N(0,1)] with population mean 16 oz. And variance 0.01 oz. What is the probability of spilling during filling?

#3. Student accumulated course points are normally distributed with standard deviation of 40. If the instructor wants the bottom of C grade cut off at 300 points, what will the class average have to be for 70% to pass with C or better?


Thanks in advance!!

 

[z3u2]

Hey guys I have a few math questions that I need help with so help me out if you can...

#1. The Army discovered that a recent shipment of grenades (both live and practice) had some labels inadvertently misapplied as to which case contained each kind. The manufacturer assured them that only 3% of the cases were labeled wrong. In a sample of 8 cases, what is the probability (show by calculation):
a) that no cases were labeled wrong
b) that no more that 1 case is labeled incorrectly.

a.
(0.97)^8

b.
probability of 0 box labeled wrong + probability of exactly 1 box labeled wrong
(0.97^8) + (8 choose 1)(0.03^1)(0.97^7)

 

[z3u2]

#2. Shampoo is sold in bottles that are labeled 16.00 ounces although they could hold up to 16.24 oz. A study of the filling process shows normal distribution [i.e. N(0,1)] with population mean 16 oz. And variance 0.01 oz. What is the probability of spilling during filling?

#3. Student accumulated course points are normally distributed with standard deviation of 40. If the instructor wants the bottom of C grade cut off at 300 points, what will the class average have to be for 70% to pass with C or better?


Thanks in advance!!

i think this two can only be estimated.
#2 is asking for what is the probability to fall outside the upper side of 2.4 standard dev.
2 std is 95%, 3 std is 99%, so there's about 4% total that falls between 2std and 3std, we are looking for the upper side of 2.4std, so it is probably ~1%

#3 is asking for what is the score that will have 20% of the students scoring between 300 and the mean, since 50% scores > mean

it's about 2/3 of std down from the mean (one std is 34% on one side, although 20% is not exactly 2/3 of 34%, but since it's a normal distribution....)
so i'd guess it to be 326

i'm wondering where u got these questions from?
they are more like from a stats course than from dat....

 

[D.D.S.]

a.
(0.97)^8

b.
probability of 0 box labeled wrong + probability of exactly 1 box labeled wrong
(0.97^8) + (8 choose 1)(0.03^1)(0.97^7)

Hey...thanks for your help... I had a question on part b here, about (8 choose 1)..can you explain to me what this is?

Thanks a lot!!

 

[Streetwolf]

#3. Student accumulated course points are normally distributed with standard deviation of 40. If the instructor wants the bottom of C grade cut off at 300 points, what will the class average have to be for 70% to pass with C or better?

So 70% have a C or better which means 30% have worse. So with 300 as our data point, 30% of the area under the curve is to the left of the data point. Then that means 20% is between the mean and 300 pts. Recall that 300 must be to the LEFT of the mean because only 30% of scores should be less than 300 and 50% of scores are less than the mean.

Many z tables show areas under a curve between the mean and the data point. Since the point is to the left of the mean we'll have a negative z score. So we just have to take the z score from the table and negate it.

Looking up an area of 0.200 (20%) we fall between -0.52 and -0.53 so I'll use -0.525 to get a better answer (your answer key might use -0.52 or -0.53 so if my answer is slightly off, try using those numbers instead and you might get the exact answer).

The formula says that Z = (data point - mean) / (std dev)

Rearranging this to solve for the mean, we have:

mean = data point - (std dev*Z)

Plugging in data point = 300, std dev = 40, and Z = -0.525, we have:

mean = 300 - (40*[-0.525])
mean = 321

Answer is ~321.


As for the shampoo problem, are you sure the std dev is 0.01 and not 0.1? Because with a std dev of 0.01, essentially 0% of the bottles should leak.

 

[z3u2]

for the shampoo problem, it is the variance that is 0.01, therefore std is 0.1

(8 choose 1) is
8!/ (7! * 1!)

it tells u how many possible combinations are there if there's 8 in total and u want exactly 1 that matches ur critaria

8! = 8*7*6*...*2*1

 

[Streetwolf]

for the shampoo problem, it is the variance that is 0.01, therefore std is 0.1

Oh snap good catch haha.

 

[D.D.S.]

Thank you guys for your help!!

 

[sublimegd]

I didnt know stats showed up on the DAT??