Problem 1

1. Problem 1 • The probability a lorry is overloaded is 0.15. The JPJ is checking 25 lorries. • What is the probability no lorry is found overloaded? • What is the probability up to 5 lorries are overloaded? • What is the probability 2 to 5 lorries are overloaded?

2. Problem 2 • On the average, 3.5 concerts are performed in Ipoh City each month. • What is the probability at least 4 concerts are performing this month? • In the suburbs Gopeng has 1.2 and Chemor has 0.8 concertes per month. What is the probability the total number of concerts in Ipoh and the suburbs is between 4 and 8 this month?

3. Problem 3 • It is estimated that only 35% of workers in a factory follow safety procedures. • During a spot check on 20 workers, (a) How many workers are expected to follow the procedures? (b) What is the probability 3 to 7 workers follow the procedures? (ii) A follow up check involves 50 workers. What is the probability 15 to 20 workers follow the procedures?

4. Problem 4 • On the average, 4 workers in a factory are promoted into managerial positions each month. • What is the probability 5 or more workers are promoted this month? • What is the probability 15 or more workers are promoted during the first quarter of the year? • What is the probability 50 or more workers are promoted this year?

5. Problem 5 • Sazali Bhd runs two factories: A with 50 workers, and B with 40 workers. 13% of workers in A and 15% in B obtain excellence citation each month. • What is the probability more than 10 workers are given excellence citations during a month? • What is the probability more workers in A are given excellence citations than B during a certain month?

6. Problem 6 • The mean daily electricity consumption of Ipoh is 5.3 million KWH, with a standard deviation of 1.1 mKWH. Assume the consumption follows the normal distribution. • What is the probability the consumption is less than 5.1 mKWH for a day? • The capacity of electricity generation is 7.5 mKWH. If this is exceeded, the city will suffer a blackout. What is the probability this happens?

7. Problem 7 • An orchard classifies its mangoes by weight. 20% of the biggest mangoes are banded as Super, the next 35% are Large, the next 30% Medium, and the rest small. If the mean weight of the mangoes is 460 g and the standard deviation is 47 g, what are the ranges of weights for each class of mangoes? (Assume the weight follows the normal distribution.)

8. Problem 8 • A supermarket gets a mean daily supply of 1250 kg of fresh vegetables, with a standard deviation of 165 kg. Its daily sale averages 1180 kg, with a standard deviation of 180 kg. Assume both supply and demand follow the normal distributions. • What is the probability the supply exceeds 1200 kg for a day? • What is the probability the demand exceeds the supply for a day?

9. Problem 9 • A study on reading speed of teenagers finds that 10% of them has a speed of more than 346 words per minutes, and 2% of them reaches a speed of 405 words and more. • Assume the speed follows the normal distribution, what is the mean and the standard deviation? • How many percent of them has a speed less than 250 words per minutes? • Five of them read in chain, with one read one minutes, then follow by another immediately. What is the probability they manage to read a total of 1800 words or more?

10. Problem 10 • The weight of a standard long loaf of bread produced by a bakery averages 560 g, with a standard deviation of 35 g. • What is the probability a loaf weighs less than the specified weight of 550g? • 5% of the bread are found to be too light due to error in mixing the dough. They are donated to charity houses. What is the range of weight for a loaf in this category. • A man bought 20 loaves for a picnic group. What is the probability the total weight is between 11.5 and 12.0 kg?