On average 20% of the bolts produced by a machine in a factory are faulty. Samples of 10 bolts are to be selected at random each day. Each bolt will be selected and replaced in the set of bolts which have been produced on that day. Given that this is a Binomial distribution:
Calculate, to 2 significant figures, the probability that, in any one sample that 2 bolt will be faulty. (5 marks)
Calculate the probability that more than two bolt will be faulty (8 marks)
Calculate the expected number of faulty bolt (3 marks)
Calculate the standard deviation of faulty bolt (5 marks)
A tennis player makes 80% of her serves accurately. We put her on the base line and ask her to serve until she misses. Let X = the number of serves the player makes before she is accurate. Given that this is a geometric distribution:
Assuming that her serves are independent, what is the probability that she will make 5 serves before she is accurate? (3 marks)
What is the probability that she misses her first free throw? (3 marks)
What is the probability that she will be accurate on the 2^{nd} or 3^{rd} serve? (7 marks)
Calculate the expected number of serves before she is accurate (3 marks)
Calculate the variance for the number of serves (3 marks)
X is a normally distributed variable with mean μ = 30 and standard deviation σ = 4. Find
P(X < 40) ( 5marks)
P(X > 21) (6 marks)
Subject | Mathematics |
Due By (Pacific Time) | 11/17/2015 12:00 am |
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