Question

A monthly demand for a new product is normally distributed with a mean of 2000 and a standard deviation of 200. For a given month, find the probability that the demand is: lebih daripada 2350. a. more than 2350. (2 Markah/Marks) b. kurang daripada 1600. Less than 1600. (2 Markah/Marks) c. di antara 1600 dan 2350 Between 1600 and 2350. (3 Markah/Marks) Apabila sesuatu pesanan diterima, masa yang diperlukan untuk penghantaran adalah selama satu bulan. Jika kebarangkalian untuk kehabisan stok ditetapkan supaya kurang daripada 0.01, When an order is placed, a month is required for delivery. If the probability that the stock will run out is set to be less than 0.01, d. kirakan amaun stok yang perlu dipesan setiap awal bulan calculate the amount of stock to order at the beginning of the month. (3 Markah/Marks) (Jumlah markah/ Total marks: 10)

Answer 1

a. more than 2350

b. Less than 1600

We are given mean 2000 standard deviation-ơ-200 We need to find P(X 2350)1- P(X2350) First we find the Zscore X- 2350-2000 Zscore_ - 2001.75 Using the normal distribution table we find pvalue P(X 2350) 0.9599 Hence the needed probability P(X>2350) 1-P(X2350) 1-0 9599#0 0401

c. Between 1600 and 2350

We are given mean 2000 standard deviation-σ-200 x1600 We need to find PX 1600) First we find the Zscore X_μ 1600-2000 Zscore 2002 Using the normal distribution table we find pvalue P(X 1600)0.0228 Hence the needed probability P(x1600) 0.0228

We are given mean 2000 standard deviation = σ = 200 We need to find P(1600 X<2350) Pl 1600X<2350) = P(X<2350)-P(X<1600) Let us find P(X<1600) X-H 1600-2000_ 200 2 score = - Using the normal distribution table we find pvalue P(X 1600)0.0228 Let us find P(X<2350) 2350-2000 -1.75 X-μ - Zscore 200 Using the normal distribution table we find pvalue P(X 2350)0.9599 Hence the needed probability Pl 1600X<2350,-P(X<2350)-P(X<1600)= 0.9599-0.0228-0.9371