Worksheet 2
A normal distribution has mean [pic]and standard deviation [pic]. Find the indicated probability for a randomly selected x-value from the distribution. (Label and shade a curve for each problem to calculate accurately.)
1) P(x ≥ ̅x)
2) P( x ≤ ̅x - 2 σ)
3) P( x ≤ ̅x + 3 σ)
A normal distribution has a mean of 18 and a standard deviation of 3. Find the probability that a randomly selected x-value from the distribution is in the given interval.
6) Label the ENTIRE normal curve with mean, standard deviations, and percentages for the situation above.
7) Between 18 and 21 8) Between 12 and 18 9) Between 15 and 24
10) At least 21 11) At least 27 12) At most 12
13) A set of 1000 values has a normal distribution. The mean of the data is 120, and the standard deviation is 20. (Draw a curve and label to answer)
a) What percent of the data is in the range 100 to 140?
b) What percent of the data is in the range 80 to 160?
c) How many values are within the limits 100 and 180?
d) How many values are greater than 140?
e) How many values are within one standard deviation from the mean?
14) Suppose the heights of adult men are normally distributed. The heights of a sample of 30 men are shown below in inches.
65, 83, 69, 67, 69, 67, 67, 72, 85, 68, 73, 65, 67, 65, 72, 71, 67, 73, 68, 72, 61, 75, 66, 78, 65, 71, 68, 76, 67, 68
a) Compute the mean and standard deviation of the sample.
b) Draw a normal curve that represents the distribution of adult male height based on the sample.
15) On the blank normal curve, label the percentages, mean, and standard deviations that are associated with it.
[pic]
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