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groverdot November 26th, 2013 06:23 PM

Intro Stats Help?
 
My prof doesn't speak English very well and she's assigned homework material that we haven't covered in class yet. Can someone walk me through the process to answer these questions?

1) "The genetics scientist, Gregor Mendel, demonstrated that the inheritance of certain traits in pea plants follows particular patterns. This study showed that one in four pea plants had purebred recessive alleles, two out of four were hybrid and one out of four was purebred dominant. Suppose we will cultivate and test some 240 pea plants. Let X be the number of pea plants that have purebred recessive alleles among the sample of 240 plants.

a) Identify the exact distribution of X and its parameter(s)
b) Justify that the distribution of this variable X can be approximated by a normal distribution
c) Identify the sampling distribution of the proportion of plants having purebred recessive alleles and its parameter(s)
d) Determine the probability that

i. More than 100 pea plants have purebred recessive alleles
ii. Less than 20% of the plants have purebred recessive alleles.
iii. Between 25% and 30% of the plants have purebred recessive alleles.
iv. Are the probabilities exact or approximate? Explain.

2) The mean and standard deviation of the wait time for customers at a bank are 5 and 1.4 minutes, respectively. Determine the probability that

a) a randomly selected customer waits 5 minutes or less.
b) the mean wait time in a random sample of 12 customers is 6 minutes or longer.
c) the mean wait time in a random sample of 36 customers is between 5.4 and 6 minutes.

3) The test scores for 300 students were entered into a computer, analyzed, and stored in a file. Unfortunately, someone accidentally erased a major portion of this file. The only information available is that 30% of the scores were below 65 and 15% of the scores were above 90. Assuming the scores are normally distributed, find their mean and standard deviation.

I've been trying for days on these and I can't make anything from them.

groverdot November 27th, 2013 12:56 PM

Re: Intro Stats Help?
 
This is what I've managed to scrounge up so far but it's not looking pretty :/

1)

a. X ~ B(240, 0.25)

b. np > 10 ---> (240)(.025) > 10 ---> 60 > 10
n(1-p) > 10 ---> (240)(0.75) > 10 ---> 180 > 10

c. X ~(approx) N(60, 6.7082)

d. (i) P(X>100)
= P(99.5 < (x-u/sigma) < 100.5
= P( (99.5-60)/6.7082 < (x-u/sigma) < (100.5-60)/6.7082)
= P(5.8883 < Z < 6.0374)
= P(Z < 6.0374) - P(Z<5.8883) I'm doing something wrong because there aren't any Z-scores for those numbers.

2)

a. X ~ N(5, 1.4) so P (X<5) = P(Z < 5-5.1.4) But you can't have a numerator of zero. What am I doing wrong?

b. Xbar ~(approx) N (5, 1.4/(sqroot12)
P(Xbar > 6) = P(Z > (6-5)/(1.4/sqroot12)
= P(Z > 2.4744)
= 1 - P(Z < 2.4744)
= 1 - 0.9932
= 0.0068 (0.68%) That looks really wrong :/

c. Xbar ~ (approx) N(5, 1.4/sqroot36)
P(5.4 < Xbar < 6) = P( (5.4-5)/(1.4/sqroot36) < (Xbar-u)/(sigma/sqrootn) < (6-5)/(1.4/sqroot36)
= P(1.7143 < Z < 4.286)
= P(Z < 4.386) - P(Z < 1.7143) And again, there aren't any Z-scores for something above 4. What am I doing wrong?

3) I actually have little to no clue as to how to approach this one. I tried going backwards with the Z-scores to get the mean/deviation but I just got myself confused and lost.

EvanJ December 5th, 2013 04:58 PM

Re: Intro Stats Help?
 
For 2A, the probability of a value being the mean or higher + the probability of a value being the mean or lower = 1 + the probability of a value being exactly the mean. The probability of a value being the mean or higher and the probability of a value being the mean or lower are equal, so if the probability of a value being exactly the mean = 0 (isn't that what continuous distributions assume?) then the answer is 0.5.


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