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3 questions I am stuck on?
Message posted by Kevin (via 204.60.249.161) on November 17, 2001 at 6:50 PM (ET)
1) the distribution of scores in the math section of a SAT in a certain year was approx. normal with a mean of 510 and the standard deviation = 112. Estimate the inter-quarile range?
2) For a population of 2000 students taking the SAT math exam, the scores on the exam have an approx. normal distribution with a mean = 590 and standard deviation = 70. Approx how many students scored between 520 and 730?
3) A dishonest coin with a probability of heads p = 0.6 is tossed n=2400 times. Calculate the chance that more than 1464 heads are obtained.
READERS RESPOND:
(In chronological order. Most recent at the bottom.)
Re: 3 questions I am stuck on?
Message posted by Mark Waters (via 128.243.220.26) on November 19, 2001 at 11:58 AM (ET)
For each question, you need to calculate the Z statistic. This is (x - mean of distribution) / standard deviation of distribution. Look up the z-value in the tables at the back of your textbook. For a question which asks for a probabuility between two values (like the one between 520 and 730) you need to work out the z-value for both 520 (which is below the mean) and 730 (above the mean). Draw yourseklf a bell-curve diagram and label the mean and the points of interest. Shade the part of the curve that represents what you want to know (e.g. the region between 520 and 730). The z-value is always less than 0.500 - half the bell-curve. If you want to know the area between 520 and 730, you need to know the area to the right of (above) 730, which is its z-value. Subtract this from 1.000 to know what the area to the left of it is. Then subtract the z-value of 520 from the value you just calculated, and there's yuor answer.For the last question you need to know the normal approximation to the binomial distribution. The SD of a binomial dist. with big n (as in this case) is square root of (npq). i.e. sqrt (2400*0.6*0.4). Now all you need to do is work out the area to the right of (above) 1464 on the bell curve. This is the probability of getting 1464 heads or more, and is the z value for that point.
Hope that helps.
Re: 3 questions I am stuck on?
Message posted by Mark Waters (via 128.243.220.25) on November 19, 2001 at 12:08 PM (ET)
Incidentally, the interquartile range is just that area between 25% and 75% of the distribution. So you need to work backwards from the Z-value (0.25) and work out the 25%- and 75%-point from therei.e. 0.25 = (x - mean)/SD
rearrange to find x.
The IQ range will be + or - x, because it is the same distance from the mean on either side (draw yourself a diagram; makes it much easier to visualise the situation)
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