A die is rolled 360 times. Let say that you want to use normal approximation to find the probability that the number of 4 was rolled less than 100 times. You need to find the probability that X<100. Explain how you would use continuity correction in this case.

  1. A card is drawn, with replacement, from a regular deck of cards 16 times. Let random variable X represent number of clubs among those 16 cards selected (there are 13 clubs in every deck; there are 52 cards in a deck). Find the variance of X,

  2. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last less than 7 months.Round to the nearest thousandth.

  3. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months.Find the probability that an instrument produced by this machine will last between 7 and 12 months. Round to the nearest thousandth.

  4. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find how long an instrument that separates the bottom 83.398% will last? Round to the nearest hundredth.

  5. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. What is the probability that the average number of months that these 100 instruments will last is greater than 12.2 months? Round to the nearest thousandth.

  6. A die is rolled 360 times. If you want to use normal approximation to find the probability that the number of 4 was rolled at least 100 times,what is the mean of the normal distribution that you would use in this case.

  7. A die is rolled 180 times. If you want to use normal approximation to find the probability that the number of 4 was rolled at least 20 times,what is the standard deviation of the normal distribution that you would use in this case

  8. A die is rolled 360 times. Let say that you want to use normal approximation to find the probability that the number of 4 was rolled less than 100 times. You need to find the probability that X<100. Explain how you would use continuity correction in this case.

  9. A die is rolled 360 times. Let say that you want to use normal approximation to find the probability that the number of 4 was rolled exactly 100 times. You need to find the probability that X=100. Explain how you would use continuity correction in this case.

  10. What is the name of the theorem that states that the sampling distribution of the sample mean is approximately normal when the sample is large?

  11. Determine whether the following random variables have a binomial distribution:

A) Ten students are chosen from a statistics class (with replacement) of 400 students. Let X be the number of students who passed the class.

B) A die is tossed three times. Let X be the sum of the three numbers obtained.

C) A coin is tossed until a head appears. Let X be the number of tosses.

only A is a binomial distribution

only B is a binomial distribution

only C is a binomial distribution

only A and B is a binomial distribution

only A and C is a binomial distribution

only B and C is a binomial distribution

all A, B, and C are binomial distributions

none is a binomial

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