Scarbo
Lv 5
Scarbo asked in 科學及數學數學 · 8 years ago

Statistics Question

Q1 A rice merchant imports a batch of pre-packed rice froman Asian country. Each sack should contain 2.5kg but some variation willinevitably occur because of the size of the lumps of rice. From record, the merchantknows that the standard deviation of each batch should be 0.15kg.The merchant plans to collect a random sample of N sacksand then finds the total weight of the rice inside them. This enableshim/her to estimate the mean weight of the rice per sack.(a) What value of N should the merchant choose if he/shewants to present the mean weight with 90% confidence ? Assuming that an error within ±0.1kg isaccepted.(b) If the mean weight per sack in the sample is 2.55kg, determine the confidence interval for the mean weight of the batch.Give your answer in 2 decimal points.Thanks!!

2 Answers

Rating
  • 8 years ago
    Favorite Answer

    (a) Z_0.05 * 0.15/√N = 0.1

    1.645 * 0.15/√N = 0.1

    N = 6.089 ~ 7

    So,N should be larger than 7

    (b) Let the mean weight of the batch is μ. The 90% C.I. is

    2.55 - 1.645 * 0.15/√5 < μ < 2.55 - 1.645 * 0.15/√5

    2.39 < μ < 2.61

  • Scarbo
    Lv 5
    8 years ago

    To myisland8132:

    Where do 0.05 and 0.1 come from?

    Thanks!

    2012-11-30 22:08:10 補充:

    To myisland8132:

    Where does 5 come from in b)?

    Thanks!

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