(b) Delicioso Pizza is concemed that the pizza diameter is not 30cm. The descrip
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Question
(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 formulac. Formulae and distribution tables are provided at the end of this examination paper refer to Appendices A and B. Table 3 Delicioso Pizza Diameter Pizza Diameter in cm Mean 28.31 0.08 28.77 29.40 Standard Deviation 1.28 Sample Variance 1.63 Standard Error Median Mode Kurtosis(0.39) Skewness Range Minimum Maximum Sum Count 5.55 25.51 31.06 7,077.05 100.00 Assuming that the sample statistics are good approximates of the population statistics and that the diameter of pizzas is distributed according to a normal distribution. State the value x where x is 2 standard deviations larger than the mean and estimate the probability (i) that the diameter of a randomly chosen pizza is larger than x. (8 marks) without assuming that the diameters of pizzas are distributed according to the normal distribution, estimate the probability that the mean (ii) diameter is larger than 31em. The sample standard deviation is estimated to be 1.28 4 marks) (ii) Explain why sampling and choosing appropriate sampling methods are (4 marks) Page 4 of 12 important in statistical analysis. BUS103e CopyTight C 2015 SIM UniversityExplanation / Answer
Solutioni:
2 standard deviations away from the mean
mean+2*stddev
=28.31+2*1.28
=30.87
P(X>30.87)
Z=x-mean/sd
P(Z>30.87-28.31/1.28)
P(Z>2)
=1-P(Z<2)
From standard normal tables
=1-0.9772
=0.0228
ANSWER:0.0228
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