A variable is normally distributed. 42% of the possible observations of the variable lie between 20 and 28. What information does this give you about the graph of the normal curve for this variable?
I am not sure how to exactly explain this. The only thing I can imagine it being is that the z-score would either be -0.02 or 0.02 because it either shades the 20-28 portion which is 42%, or shades the rest which would be 58%. I don't know if this is the right explanation for this.
As far as I am concerned. it does not give me much information. I don't know what area of the curve the 42% cut off. Is it at one end of the the distribution — either the highest or lowest portions? Is it equally spread around the mean? Is it somewhere in between these possibilities?
Unless you have some more information that you have not included, it doesn't give me adequate information to come to any conclusion.
I hope this helps. Thanks for asking.
To determine the information about the graph of the normal curve based on the given information, you can start by using the properties of the standard normal distribution.
In a standard normal distribution, the area under the curve between any two z-scores represents the probability that a random observation falls within that range.
In this case, since the variable is normally distributed, you can convert the given percentages into z-scores.
To find the z-scores corresponding to the observations of 20 and 28, you can use the Z-table or standard normal distribution calculator.
You know that 42% of the possible observations lie between 20 and 28. Therefore, you can find the z-score that corresponds to the 42nd percentile using the Z-table or calculator. Let's call this z1.
Similarly, you can find the z-score that corresponds to the 58th percentile, which represents the percentage of observations outside the range of 20 to 28. Let's call this z2.
Once you have determined the values of z1 and z2, you can plot them on the standard normal distribution graph.
Since the variable is normally distributed, the z-scores will be symmetrical around the mean. Therefore, you would expect the area between z1 and z2 to be evenly spread on both sides of the mean. This implies that the range between 20 and 28 is likely to be centered around the mean of the distribution.
In conclusion, the given information suggests that the range between 20 and 28 is likely to be evenly spread around the mean on both sides in the graph of the normal curve for this variable. However, without knowing the values of z1 and z2, we cannot determine the exact characteristics of the graph, such as the position of z1 and z2 or the standard deviation of the distribution.