B218: Suppose X is normally distributed with a mean of

1. Suppose X is normally distributed with a mean of 20 and a standard deviation of 8.

a. Determine the Z-score associated with X = 34.

b. Hence, determine the probability that X is less than 34.

2. Suppose that the time taken to drive from Orchard Road to Woodlands is normally distributed with mean 40 minutes and standard deviation 7 minutes. Determine the probability that a particular journey will take between 30 minutes and 45 minutes.

3. The temperature in Sydney in summer is normally distributed with mean 29.6 degree Celsius and standard deviation 11 degree Celsius.

a. Determine the probability that the temperaturewill change by falling more than 4 degrees Celsius in summer.

b. Determine the probability that the temperature will change by rising or falling by at least 5 degree Celsius in summer.

4. Weekly revenues for a particular curry puff seller in Ang Mo Kio are normally distributed with mean $11,480 and standard deviation $1,165. For how many weeks per year would you expect revenues to be less than $8,150?

5. The finishing times for the “National Championship – Men” category at the Singapore River Regatta 300m dragon boat race are normally distributed with mean 66.3 seconds and standard deviation 1.8 seconds.

Determine the slowest allowable time required by the RP men’s team in order to rank amongst the top 10% of all the times for the competition.

6. In a national examination, the government has designed a programme to help students at the bottom 5% of the results to improve their performances in Mathematics.

The score of the students is normally distributed with a mean of 60 marks out of a total of 100 marks and a standard deviation of 18 marks.

Determine the maximum score for a student to be eligible for this program.

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