A shipment of beach balls with a mean diameter of 28 cm and a standard deviation of 1.3 cm is normally distributed. By how many
1 answer:
Answer:
31.9 cm differs from mean by 3 standard deviations.
Step-by-step explanation:
Given:
Mean diameter of the ball = 28 cm
Standard deviation = 1.3 cm
Thus the number of standard deviations by which 31.9 cm ball size differs from the mean ball size is given by the standard normal deviate (Z) given by
Applying values we get
Thus 31.9 cm differs from mean by 3 standard deviations.
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pH = f(x) = -log₁₀x
1. Graphs
I used Excel to calculate the pH values and draw the graphs (see the Figure).
f(x) and f(x) +1 are plotted against the left-hand axis, while f(x+ 1) is plotted against the expanded right-hand axis.
The points at which pH = 0 and pH = 1 are indicated by the large red dots.
2. x = 0.5
When x = 0.5, pH ≈0.30. The point is indicated by the red diamond.
3. Transformations
(a) ƒ(x) = -log(x) + 1
This function has no y-intercept, because log(0) is undefined.
(b) ƒ(x +1) = -log(x + 1)
f(0) = -log(0 + 1) = -log(1) = 0
This function has a y-intercept at (0,0).
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