The times for a particular journey during rush hour in a certain city have a mean of 23.3 minutes and standard deviation 8.9 minutes. Using Excel or otherwise, determine the probability that the mean time taken for a random sample of 60 of the times of this journey is less than 25 minutes.

MATLAB: An Introduction with Applications
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(a) The times for a particular journey during rush hour in a certain city have a mean of 23.3 minutes and standard deviation 8.9 minutes.
Using Excel or otherwise, determine the probability that the mean time taken for a random sample of 60 of the times of this journey is less than 25 minutes.

(b) A factory produces steel sheets whose weights are known to be normally distributed with a standard deviation of 1.7kg. A random sample of 47 sheets had a mean weight of 27.3kg. Construct a 95% confidence interval for the population mean.

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