The Standard Error


The average qualifying speed for a championship NASCAR® race is 145.65 mph and the standard deviation is 9.45 mph. Only drivers who obtain z-scores greater than 1.2 will qualify for the race. If the speeds are normally distributed, what minimum speed must be clocked to compete for the trophy?

A. 146.9 mph

B. 155.2 mph

C. 157.0 mph

D. 174.8 mph


Trudy Jones recently completed her certification examination and learned that her z-score was -2.5. The examining board also informed her that a failure to pass would equal all scores that were one or more standard deviations below the mean and that those with scores higher than two standard deviations above the mean would receive a special commendation award. Trudy can conclude that she

A. failed the exam

B. needs more data to determine if she passed the exam

C. passed the exam and will receive a special commendation award

D. passed the exam, but no commendation award is forthcoming


The use of the student’s distribution requires which of the following assumptions?

A. The sample size is greater than 30.

B. The population variance is known.

C. The population is normal.

D. The sample is drawn from a positively skewed distribution.


The standard error of the sample mean is equal to 5 when n=25. If the sample size increases by a factor of four, how will the standard error change?

 A. It will be double.

B. It will be cut in half.

C. It will be cut to 1/4 of 5.

D. It will quadruple.

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