Probability & Probability Distributions

  1. The Central Limit Theorem (CLT) is one of the most important theorems in statistics. Select the most appropriate response from among the following:

    The sampling distribution of the mean may be approximated by a normal distribution, for large samples, regardless of the distribution of the parent population.

    If the population is large but not normally distributed, the distribution of sample means approaches a normal distribution provided that the sample is large.

    "It has been established mathematically that the normal distribution may be used as a basis for approximating the sampling distribution of the mean of X." This fact alone makes the normal distribution so fundamentally important in statistics

    The CLT may be used to make inferences from any population, whether the observation random variable is discrete or continuous, even if the population variance is infinite.

  2. On average, a book distributor fills orders for 1,200 books per day. If daily orders are normally distributed and the standard deviation is 120, what is the probability that a 6-day average will be between 1,000 and 1,400 books ?

    The probability is 75%

    The probability is 85%

    The probability is 90.05%

    The probability is 95.47%

  3. Given that the weights of land economists are normally distributed with mean equal to 70 kilograms and standard deviation of 10 kilograms , the probability that a certain weight will be exceeded is 0.15. What is this weight, to the nearest kilogram ?

    The weight is 110 kilograms

    The weight is 97 kilograms

    The weight is 86 kilograms

    The weight is 80 kilograms

  4. The time involved in commuting by tram from Flemington Racecourse to Latrobe Street (Melbourne) is a normally distributed variable. 95% of such commuter journeys take more than 26.75 minutes and 99% take less than 47.90 minutes. What is the mean and standard deviation of this distribution.

    Mean = 25.43, Standard deviation = 6.66

    Mean = 33.41, Standard deviation = 4.65

    Mean = 35.53, Standard deviation = 5.31

    Mean = 29.27, Standard deviation = 3.87