1)A new chemical has been found to be present in the humanbloodstream, and a medical group would like to study the presenceof this chemical in some samples of patients. The presence of thechemical in a patient is measured by a score representing the'parts per billion' in which that chemical appears in the blood. Itis known that, on this scale, men have an average score of 810.9and a standard deviation of 58. It is also known that women have anaverage score of 835.48 and a standard deviation of 21.
An assistant in the medical team has been handed a sample of 100scores. The assistant knows that all of the scores are from one ofthe two genders, but the sample was not documented very well and sothey do not which gender this is. Within the sample, the mean scoreis 825.4.
a)Complete the following statements. Give your answers to 1decimal place.
If the sample came from a group of 100 men, then the sample meanis ______ standard deviations above the mean of the samplingdistribution. In contrast, if the sample came from a group of 100women, then the sample mean is _______ standard deviations belowthe mean of the sampling distribution.
b)Based on this, the assistant is more confident that the samplecame from a group of 100 _____men or women_____
2)The life span at the birth of humans has a mean of 87.74 yearsand a standard deviation of 17.76 years. Calculate the upper andlower bounds of an interval containing 95% of the sample mean lifespans at birth based on samples of 105 people. Give your answers to2 decimal places.
a)Upper bound = _________ years
b)Lower bound = ______ years
3)A drug made by a pharmaceutical company comes in tablet form.Each tablet is branded as containing 120 mg of the particularactive chemical. However, variation in manufacturing results in theactual amount of the active chemical in each tablet following anormal distribution with mean 120 mg and standard deviation 1.665mg.
a)Calculate the percentage of tablets that will contain lessthan 119 mg of the active chemical. Give your answer as apercentage to 2 decimal places.
Percentage = %
b)Suppose samples of 12 randomly selected tablets are taken andthe amount of active chemical measured. Calculate the percentage ofsamples that will have a sample mean of less than 119 mg of theactive chemical. Give your answer as a percentage to 2 decimalplaces.
Percentage = %
4)
During its manufacturing process, Fantra fills its 20 fl ozbottles using an automated filling machine. This machine is notperfect and will not always fill each bottle with exactly 20 fl ozof soft drink. The amount of soft drink poured into each bottlefollows a normal distribution with mean 20 fl oz and a standarddeviation of 0.17 fl oz.
The Fantra quality testing department has just carried out aroutine check on the average amount of soft drink poured into eachbottle. A sample of 25 bottles was randomly selected and the amountof soft drink in each bottle was measured. The mean amount of softdrink in each bottle was calculated to be 19.90 fl oz. The FantraChief Executive Officer believes that such a low mean is notpossible and a mistake must have been made.
Calculate the probability of obtaining a sample mean below 19.90fl oz. Give your answer as a decimal to 4 decimal places.
probability =
