Would appreciate to have full working on Question b i (a) Delicioso Pizza Pte Lt

Question

Would appreciate to have full working on Question b i

(a) Delicioso Pizza Pte Ltd sells 12-inch or 30 cm pizzas in outlets around the county. To predict future orders, a sample of 250 transactions were collected and analysed. The relative frequencies are listed in Table 2. Table2 To 34% 34% 16% 16% Hawaiian Verify that the relative tequences shown here can be interpreted as a legitimate assignment ofprobabilities for the 4 lavours offered 3 marks) Page 3 of 12 (T) Identify the probability that a randomly chosen pizza has 3 marks) not have a 3 marks) (i) Identify the probablity that a randonly chosen pizza does Supreme topping. b) Delicioso Pizza is concemed that the pizza diameter is not 30cm The descriptive statistics on pizza diameter is provided in Table 3. For the following questions, you may need to use some forumalae. Formlae and distribution tables are provided at the end of this examination paper - refer to Appendices A and B.

Explanation / Answer

Question (b)

(i) Here we see that there is normal distribution

Estimated Population mean = sample mean = 28.31

Estimated population standard deviation = sample standard deviation = 1.28

so here X = 28.31 + 2 * 1.28 = 30.87

So, writing question in mathematical notation

Pr( x > 30.87; 28.31; 1.28) = Pr(Z > 2) = 0.0228

(b) Here we are not assuming that diameter of pizzas are distributed as per normal distribution.

sample standard deviation = 1.28

standard error = 0.08

here we will use t - distribution

so Pr( > 31) = Pr ( t > (31 - 28.31)/0.08) = Pr( t > 33.625) = 0.0000

so there isno probability that it is 0 that means is greater than 31

(c) Here sampling methds are important because samples are representative of population. so insteasd of doing observational study or experiment on whole population, we do take samples to infer results about population

here appropriate samplingmethods are necessary as depends on the research question. Sometime, we require cluster sampling, sometimes simple random sampling , it all depends on what results we want to achieve

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