Find two numbers that add up to 158. The greater number is 40 more than the lesser number

The XO Group Inc. conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of

slavikrds [6]

Answer:

a) 0.0392

b) 0.4688

c) At least $39,070 to be among the 5% most expensive.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 29858, \sigma = 5600$

a. What is the probability that a wedding costs less than $20,000 (to 4 decimals)?

This is the pvalue of Z when X = 20000. So

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

$Z = \frac{20000 - 29858}{5600}$

$Z = -1.76$

$Z = -1.76$ has a pvalue of 0.0392.

So this probability is 0.0392.

b. What is the probability that a wedding costs between $20,000 and $30,000 (to 4 decimals)?

This is the pvalue of Z when X = 30000 subtracted by the pvalue of Z when X = 20000.

X = 30000

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

$Z = \frac{30000 - 29858}{5600}$

$Z = 0.02$

$Z = 0.02$ has a pvalue of 0.5080.

X = 20000

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

$Z = \frac{20000 - 29858}{5600}$

$Z = -1.76$

$Z = -1.76$ has a pvalue of 0.0392.

So this probability is 0.5080 - 0.0392 = 0.4688

c. For a wedding to be among the 5% most expensive, how much would it have to cost (to the nearest whole number)?

This is the value of X when Z has a pvalue of 0.95. So this is X when Z = 1.645.

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

$1.645 = \frac{X - 29858}{5600}$

$X - 29858 = 5600*1.645$

$X = 39070$

The wedding would have to cost at least $39,070 to be among the 5% most expensive.

5 0

2 years ago

Tristan records the number of customers who visit the store each hour on a Saturday. His data representing the first seven hours

vredina [299]

First, list the numbers from smallest to greatest:
12, 15, 18, 20, 23, 23, 28
Median is the middle number of the list—20.

4 0

2 years ago

Read 2 more answers

A computer randomly selects a letter from the alphabet.

Nikolay [14]

1) 26 different outcomes are in the sample space.

2) 1 / 26 is the probability that the computer produces the first letter of your first name.

Step-by-step explanation:

1) You have to find out the different outcomes in the sample space :

A "Sample space" is defined as the set of all the possible outcomes of an event.
Here, the given event is randomly selecting a letter from the alphabets.

Therefore, the sample space must contain all the possible alphabets that can be chosen randomly.

The sample space is the set of all the 26 alphabets in English language.

⇒ Sample space = {A,B,C,D...........,Y,Z}

⇒ 26 different outcomes.

2) The probability the computer produces the first letter of your first name :

Here, the required outcome is getting the first letter of your first name.

Probability = No. of required outcomes / total no. of outcomes.

For example, The name Alex Davis has the first letter of the fist name as alphabet 'A'.

∴ Probability = 1 / 26

Similarly, for any first name there is going to be any one alphabet from the 26 alphabets, thus the probability to get the first letter will be always 1 / 26.

7 0

2 years ago

In a café, drinks are priced according to what size they are.

Andrei [34K]

A) Gavin’s drinks altogether cost £9.00
1.50+2.50x3
=1.50+7.50
=£9.00
b) Lian gets back £3.50
1.50+2.00+3.00
=6.50

10.00-6.50=£3.50

8 0

2 years ago

The sound intensity of rustling leaves is 100 times the reference intensity. Use your graph to determine the sound intensity of

wariber [46]

The sound intensity of rustling leaves, y = 20 decibels

Step-by-step explanation:

y = 10logx

The sound intensity of rustling leaves is 100 times the reference intensity.

x = ratio of intensity of sound to reference to intensity

x = 100:1 or x = 100

y = 10 log(100) = 10 * 2 = 20 decibels

y = 20 decibels

4 0

2 years ago

Read 2 more answers