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Math Help - Intro Stats Help?

  1. #1
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    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.
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  2. #2
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    Re: Intro Stats Help?

    Hi Groverdot
    You must be able to do 2A. just think a little.
    Maybe you could have a go at some of the others, why don't you show the forum what you have attempted.
    My stats knowledge is very rusty, I'd have to do some research but some of the other questions don't look like they would be that hard.
    I think in 2b and 2c you would have to find the new standard deviation for the sample size and then find the z score and then use your z-score tables to find areas (probabilities). Like I said, my stats knowledge is poor. But have a go yourself and show the forum what you CAN do.
    Melody
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  3. #3
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    Re: Intro Stats Help?

    Problem 1 is about the binomial distribution. You'll want to read up on that before trying it.

    If I had to guess I'd say that problem 2 is the normal distribution. You need to understand how to take the mean and standard deviation to normalize things and then use the CDF of the normal distribution (usually in lookup tables) to answer a-c.

    3 is also the normal distribution. By the time you figure out how to do 2 you'll be able to do 3.
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  4. #4
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    Re: Intro Stats Help?

    Allrighty, but it's not gonna look too pretty :P

    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.
    Last edited by groverdot; November 27th 2013 at 12:54 PM. Reason: Make it look like less of an eyesore
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  5. #5
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    Re: Intro Stats Help?

    ok Please humour me by answering these questions.

    A very large group of children do a test. The average mark is 60.0001
    What percentage gets 60 or less than 60?
    What percentage gets more than 60?
    If one child is chosen at random what is the probability that her/his score will be 60 or less than 60?
    If one child is chosen at random what is the probability that her/his score will be more than 60?
    What is another word for average?
    Now do 2a.
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