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lukranit [14]
3 years ago
11

The time it takes a customer service complaint to be settled at a small department store is normally distributed with a mean of

10 minutes and a standard deviation of 3 minutes. Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.
Mathematics
1 answer:
noname [10]3 years ago
5 0

Answer:

0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 10 minutes and a standard deviation of 3 minutes

This means that \mu = 10, \sigma = 3

Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.

This is 1 subtracted by the p-value of Z when X = 15, so:

Z = \frac{X - \mu}{\sigma}

Z = \frac{15 - 10}{3}

Z = 1.67

Z = 1.67 has a p-value of 0.9525.

1 - 0.9525 = 0.0475.

0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.

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The distribution of the scores on a certain exam is ​N(40​,5​), which means that the exam scores are Normally distributed with a
katen-ka-za [31]

Answer:

Step-by-step explanation:

Let x represent the random variable representing the scores in the exam. Given that the scores are normally distributed with a mean of 40 and a standard deviation of 5, the diagram representing the curve and​ the position of the​ mean, the mean plus or minus one standard​ deviation, the mean plus or minus two standard​ deviations, and the mean plus or minus three standard deviations is shown in the attached photo

1 standard deviation = 5

2 standard deviations = 2 × 5 = 10

3 standard deviations = 3 × 5 = 15

1 standard deviation from the mean lies between (40 - 5) and (40 + 5)

2 standard deviations from the mean lies between (40 - 10) and (40 + 10)

3 standard deviations from the mean lies between (40 - 15) and (40 + 15)

b) We would apply the probability for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 40

σ = 5

the probability that a randomly selected score will be greater than 50 is expressed as

P(x > 50) = 1 - P( ≤ x 50)

For x = 50,

z = (50 - 40)/5 = 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.98

P(x > 50) = 1 - 0.98 = 0.02

7 0
3 years ago
The number of people who have heard a rumor often grows exponentially. Consider a rumor that starts with 3 people and where the
Marysya12 [62]

Answer:

3.9125 × 10⁵² people

Step-by-step explanation:

A rumor starts with 3 people and the number of people who heard it doubles each day.

How many people would have heard the rumor after 20 days?

To calculate exponential growth, we use the formula:

y (t) = ae^{kt}

where;

a = value at the start =3

k = growth rate = 2×3 = 6

t = time = 20 days

y(t) = value of the population at the given time (t) =??

y(t) = 3 \times e^{6\times 20}

y(t) = 3.9125 × 10⁵² people

4 0
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The number of Atlantic blue fin tuna in thousands can be modeled by P(x)=230(.881)^x where X represents the number of years sinc
Maurinko [17]
<h3>Answer: 1981</h3>

===================================

Work Shown:

Recall that P is in thousands, so P = 95 means 95,000.

Plug in P(x) = 95. Solve for x. Use logarithms to get this done.

P(x)=230(0.881)^x

95=230(0.881)^x

95/230 = (0.881)^x

0.41304347826087 = (0.881)^x

(0.881)^x = 0.41304347826087

Log( (0.881)^x )= Log( 0.41304347826087 )

x*Log( 0.881 )= Log( 0.41304347826087 )

x= Log( 0.41304347826087 )/Log( 0.881 )

x= 6.97883817154785

x= 7

Approximately 7 years after 1974 is when the population will be around 95,000.

7 years after 1974 = 1974+7 = 1981

8 0
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Ruby wants to buy a bag that costs Php 675.95. If she has saved Php 148.50 for it, how much more does she need?
Akimi4 [234]

Answer:

527•45 is the answer brother

7 0
3 years ago
Explain in words how to find the product of -4 (-1.5) using a number line.where do you end up
Ierofanga [76]

Answer:

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the answer is  6

Three numbers like -1 x  4 will also be 2 numbers of negative.

= -4

We change this to -4 x 1.5 and shows the answer as -6

But the question had 2 negative numbers already and the answer is just positive 6.

8 0
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