The IQ of 100 college students in XYZ univ are found to be normally distributed where mean is 105 and standard deviation is 8. If the student IQ score is 90, what is the probability that another student randomly slected has an IQ score of below 90.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the probability related to that Z score.
3-100
Matthews, Young and Associates, a Chapel Hill consulting firm, has these records indicating the number of days each of its ten staff consultants billed last year:
212 320 230 210 229 231 219 221 222
a)Without computing the value of any of these measures, which of them would you guess would give you more information about this distribution: range or standard deviation?
b) Considering the difficulty and time of computing each of the measures you reviewed in part (c), which one would you suggest is better?
(d) What will cause you to change your mind about your choice?
To find the probability that a randomly selected student has an IQ score below 90, we can use the Z-score formula and the standard normal distribution.
1. Calculate the Z-score:
The Z-score measures the distance between a given value and the mean, in terms of standard deviations. It is calculated using the formula:
Z = (X - μ) / σ
where X is the value, μ is the mean, and σ is the standard deviation.
In this case, the mean (μ) is 105, the standard deviation (σ) is 8, and the value (X) is 90.
Z = (90 - 105) / 8
Z = -15 / 8
Z ≈ -1.875
2. Find the probability using the Z-table:
The Z-table provides the cumulative probability for any given Z-score. We can use the table to find the probability associated with a Z-score of -1.875.
Since the Z-table provides the cumulative probability up to a specific Z-score, we want to find the probability from negative infinity to -1.875 (the left side of the distribution curve).
Looking up the Z-score of -1.875 in the Z-table, we find that the corresponding cumulative probability is 0.030.
3. Interpret the probability:
The probability that a randomly selected student has an IQ score below 90 is approximately 0.030, or 3%.