<span>The distribution of a data set is indicated by the standard deviation, and the range can serve as an estimate for this characteristic. Consequently, Set b (100, 140, 150, 160, 200, 10, 50, 60, 70, 110) exhibits the greatest standard deviation due to its 190 range (i.e., 200 - 10).</span>
Begin by creating a system of equations: let 'a' represent the amount Mary earns per student, and 'b' denote her fixed amount. The equations are 90=15a+b (subtracting the lower from the upper equation) and 62=8a+b. From these, we have 90-62=28, leading to 15a-8a=7a, and b cancels itself out. This gives us 7a=28, resulting in a=4. Substituting 'a' into 62=8a+b reveals b=30. Since Lisa earns half of Mary's base, her fixed amount is 15, but she makes twice as much per student, bringing her rate to 8 per student. Thus, we can formulate: m=4c+30 for Mary's earnings, and l=8c+15 for Lisa's. Setting c=20 results in m=110 and l=175, showing that Lisa makes more when teaching a class of 20 students. I trust this information helps.
Answer:
0.0359
Step-by-step explanation:
Provided values:
Mean durations of three independent processes are 15, 30, and 20 minutes.
The associated standard deviations are 2, 1, and 1.6 minutes, respectively.
Thus,
New Mean = 15 + 30 + 25 = 65
Variance = (standard deviation)²
or
Variance = 2² + 1² + 1.6² = 7.56
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Standard deviation = √variance
or
Standard deviation = 2.75
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Z-value = 
or
Z-value = - 1.81
Consulting the Z-table, the Probability of Z ≤ -1.81 is equal to 0.0359.
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