Ask Experts Questions for FREE Help !
Ask
    cowgirl3's Avatar
    cowgirl3 Posts: 5, Reputation: 2
    New Member
     
    #1

    Feb 25, 2011, 08:39 PM
    Probabilities of Normal distribution
    I am looking for some help on probabilites of Normal Distributions:

    Suppose it is know that the distibution of purchase amounts by customers entering a popular retail store is approximately normal with a mean of $25 and standard deviation of $8.

    a)Find the dollar amount such that 75% of all customers spend no more than this amount
    b) Find the dollar amount such that 80% of all customers spend at least this amount
    c) Find two dollar amounts, equidistant from the mean of $25 such that 90% of all customers purchases are between these values.

    I am using the NORMINV function in excel to answer these questions where the first input is probability (x).

    My question is for part a, can someone clarify if the probability should be 0.75 or 0.25 (1-.75). I think it should be 0.75

    For part b, can someone clarify if the probability should be 0.80 or 0.20 (1-.80). I think it should be 0.20

    I am confused between the wording of "Spend no more than" and "spend at least" for part a and b.

    For part c, I am not quite sure what I should be doing.

    Any help would be appreciated.

    Thanks!
    jcaron2's Avatar
    jcaron2 Posts: 986, Reputation: 204
    Senior Member
     
    #2

    Feb 25, 2011, 09:18 PM
    Cowgirl, you're correct about parts (a) and (b). For part (c), they're asking you to find the middle 90%. In other words, what are the values corresponding to 5% and 95%? 90% of the customers spend amounts between those two values.
    cowgirl3's Avatar
    cowgirl3 Posts: 5, Reputation: 2
    New Member
     
    #3

    Feb 26, 2011, 10:25 PM
    So for part C, I found the z score for 90% confidence interval which is 1.65. To find the upper and lower values, I used the equation:
    mean (+/- ) z score * standard deviation. So the answers I came up with are $11.80 ($25 - (1.65* $8)) and $38.20 ($25 + (1.65 *$8). Can anyone confirm if I am on the right track with this answer.

    Thanks so much!
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
     
    #4

    Feb 27, 2011, 02:29 AM

    Well, I don't know how to use the confidence interval method, but when I do it using the normal table, I get something very close to your answer. I guess yours is good then :) (My z score is 1.645 while yours is 1.65)

    Anyway, the mean is at 50% of the people.

    Since the question asks for the amounts equidistant from the mean, such that you get 90% of the people, it means that there is 90/2 = 45% to the right of the mean and 45% to its left.

    Now, my normal table gives me the probabilities to the left of the amount. 45% right of the mean is at the 45+50 = 95 percent amount.

    That is from a z-score of 1.645.

    Converting this to amounts in dollar, I get:





    And the other lower value is

Not your question? Ask your question View similar questions

 

Question Tools Search this Question
Search this Question:

Advanced Search

Add your answer here.


Check out some similar questions!

Normal distribution [ 1 Answers ]

Hi can you please help me , I don't know how to do this question. Thanks. Q/ If X and S^2 (where S^2 =1( ) 21nX Xnii) are the sample mean and sample variance of a random sample of n = 30 elements from a Normal population, N(9,100), find: (I) P(40< S^2 <150)

Normal distribution [ 3 Answers ]

On the same diagram sketch three normal distributions, one with mean 0 and standard deviation 2, one with mean 0 and standard deviation 4, and one with mean 3 and standard deviation 2. Make sure that you label each of the three graphs. I do not understand how I am supposed to do this, can...

Normal distribution [ 1 Answers ]

A politician wants to know what percentage of the voters support her position pn the issue of forced busing for integration. What size voter sample should be obtained to determine with 90 % confidence the support level to within 4%? Given that 10% of the nails using a certain manufacturing...

Normal distribution [ 1 Answers ]

for a normal distribution problem: mean = 100 standard deviation = 10 80% of the values are between what 2 x values symmetrically distributed around the mean. How can you find the answer?


View more questions Search