12. An orange has a mean diameter of 10cm with a standard deviation of 0.51cm. What is the probability of an orange will smaller than I1.2cm and the probability of the orange bigger than 11.2cm?
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- Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0°C and 2.679°C.The average price of a kilogram of ham is P1,300. Assume that the standard deviation is P150. If a random sample of 30 one-kilogram packages is selected, find the probability that the mean sample will be less than P1,160. Show the complete solution.Two devices are used to measure the length of beam. If the true length of the beam is L, the measurement error made by one device, E, , is normally distributed with mean 0 and standard deviation 0.006L, and the measurement error made by the other device, E, , is normally distributed with mean 0 and standard deviation 0.004L. The two measurement errors are independent of each other. What is the probability that the average value of the two measurements, (E, + E,)/2, is within 0.5% of L? Note that this problem can be done using the attached table of the cdf of the standard normal random variable.
- Suppose the weight of watermelons produced in Adana follows the normal distribution with mean 7.2 kg and standard deviation 2.4. Find the proportion of these watermelons that weight heavier than 7.5kg. If we randomly select one of these watermelons, find the probability that its weight will be less than 7kg.Birthweight at a hospital were reported to have a mean of 3668 grams (g) and a standard deviation of 511 g. These birthweights are normally distributed. Find the probability that a single baby's birth weight was less than 4000 g.Malaysian families recorded an average of 17.2 kg of glass garbage each year with the standard deviation of the distribution is 2.5 kg. Using a central limit theorem, compute a probability that the mean of a sample of 55 families will be between 17 kg and 18 kg.
- It is known that the mean blood pressure of a community is 125 mm of Hg with a standard deviation of 3 mm of Hg. What would be the probability of finding individuals with blood pressure less than 120 mm of Hg in the community? ( Assume blood pressure is normally distributed).Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than -0.71°C.The vacation leave time of employees in a firm in a month is normally with a mean of 100 hours and a standard deviation of 20 hours. 1. Find the probability that the vacation – leave time of an employee in a month exceeds 180 hours.
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