HSC Standard 2 The Normal Distribution 1

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The results of Mathematics exam were normally distributed.Betty gained a z-score of -2 .What percentage of students scored better than Betty?

1 point

84%

97.5%

95%

2.5%

Clear selection

The pulse rates of a large group of 18-year-old students are approximately normally distributed with a mean of 75 beats/minute and a standard deviation of 11 beats/minute. What percentage of 18-year-old students have pulse rates less than 75 beats/minute?

1 point

32%

50%

68%

84%

Clear selection

In a normally distributed set of scores, the mean is 70 and the standard deviation is 6. Approximately what percentage of the scores will lie between 58 and 82?

1 point

34%

68%

95%

99.7%

Clear selection

In a normally distributed set of scores, the mean is 23 and the standard deviation is 5. Approximately what percentage of the scores will lie between 18 and 33?

1 point

34%

47.5%

68%

81.5%

Clear selection

Betty’s z–score on a particular test was 1.5. If the class average and standard deviation were 64 and 8 respectively, Betty’s mark was:

1 point

65.5

Clear selection

A set of data is normally distributed with a mean of 48 and a standard deviation of 3. Approximately what percentage of the scores lies between 39 and 45?

1 point

15.85%

31.7%

47.5%

49.85%

Clear selection

The number of hours worked during a week by casual staff in the hospitality industry is normally distributed with a mean of 18 hours and a standard deviation of 2.5 hours. What is the percentage of casual staff working fewer than 23 hours in a week?

1 point

84%

95%

47.5%

97.5%

Clear selection

In a class, the shoe sizes of the students are normally distributed. The mean shoe size of these students is 6.5 and the standard deviation is 2. Approximately what percentage of the class has a shoe size larger than 8.5?

1 point

16%

34%

68%

84%

Clear selection

There will be 90 000 students sitting an examination. If their examination results form a normal distribution, how many students would be expected to score a result between 1 and 2 standard deviations above the mean?

1 point

12 150

24 300

30 600

42 750

Clear selection

The scores on an examination are normally distributed with a mean of 70 and a standard deviation of 6. Michael received a score on the examination between the lower quartile and the upper quartile of the scores. Which shaded region most accurately represents where Michael’s score lies?

1 point

Clear selection

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