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12. The p.d.f of a continuous random variable is give
P(x) = kx (1-x) e^x, 0 ≤ x ≤ 1 find k hence find mean and standard deviation
=
A machine fills boxes with chocolate balls. The weights of the empty boxes are normally
distributed with a mean of 150 g and a standard deviation of 10 g. The mean weight of each
chocolate ball is 40 g with a standard deviation of 0.8 g. A full box contains 25 chocolate balls.
A medical investigation claims that the average number of infections per week
at a hospital is 16.3. A random sample of 10 weeks had a mean number of 17.7
infections. The sample standard deviation is 1.8. Is there enough evidence to
reject the investigator’s claim at α = 0.05? Assume the variable is normally
distributed.
(a) If P− value ≤ α, reject the null hypothesis.
(b) If P− value ≥ α, do not reject the null hypothesis.
A machine fills boxes with chocolate balls. The weights of the empty boxes are normally
distributed with a mean of 150 g and a standard deviation of 10 g. The mean weight of each
chocolate ball is 40 g with a standard deviation of 0.8 g. A full box contains 25 chocolate balls.
a. Calculate the mean weight of a full box of chocolate balls
b. Calculate the standard deviation of the weight of a full box of chocolate balls.
c. Calculate the probability that a full box of chocolate balls weighs less than 1140 g.
d. The company also produces boxes of chocolate squares. It was found that 19% of the boxes
weigh less than 800 g and 28% weigh more than 1200 g. Calculate the mean and standard
deviation of the weight of these boxes
A sample of size 60 is taken from a population of chocolate balls. The weights of chocolate balls are normally distributed with a mean of 40 g and a standard deviation of 8 g. a. Find the parameters for this distribution of the sample mean. b. Find the probability that the sample mean is between 38 g and 42
A machine fills boxes with chocolate balls. The weights of the empty boxes are normally
distributed with a mean of 150 g and a standard deviation of 10 g. The mean weight of each
chocolate ball is 40 g with a standard deviation of 0.8 g. A full box contains 25 chocolate balls.
a. Calculate the mean weight of a full box of chocolate balls
b. Calculate the standard deviation of the weight of a full box of chocolate balls.
c. Calculate the probability that a full box of chocolate balls weighs less than 1140 g.
d. The company also produces boxes of chocolate squares. It was found that 19% of the boxes
weigh less than 800 g and 28% weigh more than 1200 g. Calculate the mean and standard
deviation of the weight of these boxes
here is a notice in a lift saying that the maximum weight allowed is 1200 kg. The weights of passengers are normally distributed with a mean of 76 kg and a standard deviation of 9.5 kg. 15 passengers get into the lift. a. Calculate the mean and standard deviation of the total weight of 15 passengers. b. Is it likely that the lift will be overloaded with 15 passengers? Show some calculations to support your answer
A machine fills boxes with chocolate balls. The weights of the empty boxes are normally distributed with a mean of 150 g and a standard deviation of 10 g. The mean weight of each chocolate ball is 40 g with a standard deviation of 0.8 g. A full box contains 25 chocolate balls. a. Calculate the mean weight of a full box of chocolate balls b. Calculate the standard deviation of the weight of a full box of chocolate balls. c. Calculate the probability that a full box of chocolate balls weighs less than 1140 g. d. The company also produces boxes of chocolate squares. It was found that 19% of the boxes weigh less than 800 g and 28% weigh more than 1200 g. Calculate the mean and standard deviation of the weight of these boxes
There is a notice in a lift saying that the maximum weight allowed is 1200 kg. The weights of
passengers are normally distributed with a mean of 76 kg and a standard deviation of 9.5 kg.
15 passengers get into the lift.
a. Calculate the mean and standard deviation of the total weight of 15 passengers.
b. Is it likely that the lift will be overloaded with 15 passengers? Show some calculations to
support your answer
