What was the probability of selling 4 or less? (d) The average sales of apples i

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What was the probability of selling 4 or less? (d) The average sales of apples is 5000 with a standard deviation of 500. (1) What is the probability that sales will be greater than 5500 apples? (2) What is the probability that sales will be less than 4900 apples? (3) What is the probability that sales will be less than 4250 apples? The following question involves learning/employing research skills out data on the Internet, presenting it in a well constructed and informative table, and calculating some probabilities showing calculation methods. 1. Search the Internet for the latest figures you can find the age on sex of the Australian population. 2. Then using Excel, prepare a table of population numbers (not percentage) by sex (in the columns) and age (in the rows). Break age into about 5 standard groups, e.g. 0-14, 15-24, 25-54, 55-64, 65 and over. Insert total of each row and each column. Paste the table into Word as a picture. Give the table a title, and below the table quote the source of the figures. 3. Calculate from the table, showing your calculation methods: The probability that any person selected at random from the population is a male. The probability that any selected at random from the population is aged between 15 and 24. The joint probability that any person selected at random from the population is a female and aged between 15 and 34. The conditional probability that any person selected at random from the population is 25 or over given that the person is a male. Show all calculations/reasoning A company wishes to set control limits for monitoring the direct labour time to produce an important product. Over the past the mean time has been 20 hours with a standard deviation of 10 hours and is believed to be normally distributed. The company propose to collect random samples of 64 observations to monitor labour time. 1. 1 If management wishes to establish x? control limits covering the 95% confidence interval, calculate the approximate UCL and LCL. 2. If management wishes to use smaller samples of 16 observations calculate the control limits covering the 95% confidence interval. 3. Management is considering three alternatives procedures in order to maintain tighter control over labour time: Sampling more frequency using 16 observations and confidence intervals of 90% Maintaining 95% confidence intervals and increasing sample size to 64 observations Setting 95% confidence intervals and using sample sizes of 36 observations. Calculate the control limits for each of the 3 alternatives.

Explanation / Answer

avg =5000 sd=500

1)p(x>5500) =p(z> 5500-5000/500)=p(z>1)=1-p(z<1) =   1- 0.841345= 0.158655

2)p(x<4900) =p(z< 4900-5000/500)= p(z<-0.2) = 0.42074

3)p(4250) = p(z< 4250-5000/500) =p(z< -1.5) = 0.066807

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