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Nitella [24]
3 years ago
12

Hungry Howies, a local pizza delivery chain, wants to provide the best service possible for its customers. They decide to record

the delivery times 100 randomly selected days, taking the average each day. The resulting distribution is approximately normally with an overall mean of 31.2 minutes.
(a) On one randomly selected day the average delivery time was 34 minutes, which is 0.43 standard deviations above the mean. What is the standard deviation of the distribution?
Advanced Placement (AP)
1 answer:
Olin [163]3 years ago
5 0

Answer:

6.5 minutes

Explanation:

We solve this question using this z-score formula.

z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation

z = standard deviations above the mean = 0.43

x = 34 minutes

μ = 31.2 minutes

σ = unknown

n = 100

0.43 = (34 - 31.2)/ σ

0.43 = 2.8 / σ

Cross Multiply

0.43 × σ = 2.8

σ = 2.8/0.43

σ = 6.511627907

The standard deviation of the distribution is approximately 6.5 minutes

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Answer:

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Explanation:

Let's analyze each statement given.

1. f has an inflection point at x = -1.5 --> TRUE

An inflection point is a point in which the function f(x) changes concavity: this means that the first derivative of a function has a relative minimum or maximum, and therefore the second derivative is zero, f''(x_0)=0.

In this case, we see that at the point

x = -1.5

The first derivative is flat: this means that at this point, the second derivative is zero, so this is an inflection point.

2. f is increasing on the interval from x = -3.2 to x = -4.5. --> FALSE.

We simply don't know this: in fact, we cannot see the graph of the derivative between -4.5 and -3.2, therefore we don't know if the function is increasing or not.

3. f has a relative minimum at x = 1.5 --> FALSE.

A function f(x) has a relative minimum at a point x_0 if the first derivative f'(x) is zero at that point:

f'(x_0)=0

and moreover, the derivative is negative on the left of the point and positive on the right of the point.

This is not the case: in fact, we see that at x = 1.5 the first derivative is not zero, therefore this statement is not true.

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3 years ago
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const2013 [10]

Answer:

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Explanation:

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