Let x be a normally distributed continuous random variable with a mean of 52 and a standard deviation of 7.5. Determine the value of x such that the area to the left of x is 0.0367. Round the solution to two decimal places, if necessary. x=

SAT college entrance test scores are known to be a normally distributed with a mean of 1009 and a standard deviation of 59. Determine the 65th percentile of all SAT scores. Round the solution to the nearest whole number, if necessary. The 65th percentile is

An honor society on campus only accepts the top 9% of students (according to GPA). If the GPAs of all students on campus are known to be a normally distributed with a mean of 2.83 and a standard deviation of 0.42, determine the minimum GPA a student must achieve in order to be admitted to the honor society. Round the solution to two decimal places, if necessary. A minimum GPA of is required for admission to the honor society.

A soft drink machine at a local fast food restaurant can be calibrated so that it dispenses an average of ounces per cup. If the ounces of soda dispensed are normally distributed with standard deviation 1.3 ounces, find a value of such that 24-ounce cups will overflow only 10% of the time. Round the solution to one decimal place, if necessary. = ounces