Expert: Sherry Wallin - 8/4/2010

Question
From a set of 1000 observations known to be normally distributed, the mean is 534 cm and SD is 13.5 cm.  How many observations are likely to exceed 561 cm? How many will be between 520.5 cm and 547.5 cm? Between what limits will the middle 50% of the observations lie?

Answer
Hi Harshad~

What do you know about statistics? It is hard for me to help you with a question if you don't show me what you have tried or tell me what you know. 561 is 2 standard deviations to the right. From 534 to 547.5 is within 1 standard deviation and from 547.5 to 561 is 2 standard deviations so for x > 561 you are in the third standard deviation. The empirical rule tells us that in a normal distribution that 99.7% of the data falls within 3 standard deviations. And 95% of the data are within 2 standard deviations. You want the right hand half so you can think of the it as looking at the last 5% and only 2.5% of that is in the tail on the right. So what is 2.5% of 1000? 25

The middle 50% of observations will be 25% to the right of the mean and 25% to the left of the mean. Convert to a z-score and then find out how many standard deviations this is. If you still need help please ask.

Math Prof