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photoshop1234 [79]
3 years ago
8

Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. Consider a sample of

ten randomly selected people who recently booked an airline ticket. What is the probability that at least nine out of ten people used an online travel website when they booked their airline ticket
Mathematics
1 answer:
ExtremeBDS [4]3 years ago
3 0

Answer:

0.183

Step-by-step explanation:

This is a question on Binomial Probability

Formula =nCx × p^x × q^n - x

p = 0.72

q = 1 - p

= 1 - 0.72

= 0.28

x = number of successes = 9

n = 10

The probability that at least nine out of ten people used an online travel website when they booked their airline ticket

At least 9 out of 10 means

x ≥ 9 = x = 9 and x = 10

Hence,

P(x ≥ 9) = 10C9 × (0.72^9 × 0.28^10 - 9) + 10C10 × ( 0.72^10 × 0.28^10 - 10)

P(x ≥ 9) = 0.14559635388 + 0.0374390623

= 0.18303541631

≈ 0.183

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The manager at a sports radio station will be covering several football games over the weekend. She knows that most of her liste
Paraphin [41]

Complete Question:

The manager at a sports radio station will be covering several football games over the weekend. She knows that most of her listeners are at least 22 years old and wants to know what age group she should gear her advertisements to for the games. She takes a random sample of 46 listeners from age 22-39 and 57 listeners who are 40 and older and asks them if they are likely to tune in to football games. The "yes" responses are recorded in the file attached below.

1. At the 0.05 level of significance, is there a significant difference in the proportion of listeners based on age?

2. Is there evidence to suggest that there is a significant difference in the proportion of listeners based on age?

Answer:

1) There is no significant difference in the proportion of listeners based on age

2) No, there is no evidence

Step-by-step explanation:

Sample size of group 1, n_1 = 46

Sample size of group 2, n_2 = 57

Number of Yes in group 1,  X_1 = 32

Number of Yes in group 2, X_2 = 47

Proportion of Yes in group 1:

\hat{p_1} = \frac{X_1}{n_1} \\\hat{p_1} = \frac{32}{46}\\\hat{p_1} = 0.6957

Proportion of Yes in group 2:

\hat{p_2} = \frac{X_2}{n_2} \\\hat{p_2} = \frac{47}{57}\\\hat{p_2} = 0.8246

Null Hypothesis, H_0: p_1 = p_2

Alternate Hypothesis,H_a: p_1 \neq p_2

\hat{p} = \frac{X_1 + X_2}{n_1 + n_2}  \\\\\hat{p} = \frac{ 32+47}{46+57} \\\\\hat{p}= 0.767

Significance level,

Calculate the test statistic

z = (\hat{p_1} - \hat{p_2})/\sqrt{(\hat{p} * (1-\hat{p}) * (\frac{1}{N_1}  + \frac{1}{N_2})}\\\\z = (0.6957-0.8246)/ \sqrt{(0.767*(1-0.767)*(1/46 + 1/57))}\\\\z = -1.54

Get the P-value from the probability distribution table:

At z = -1.54, P-value = 0.1236

Since (P-value = 0.1236) > (α = 0.05), we will accept the null hypothesis. This means that there is no evidence to suggest that there is difference in the proportion of listeners based on age.

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2 years ago
Find the distance between the two points rounding to the nearest tenth (if
lana [24]

Answer:

5.7

Step-by-step explanation:

Creating the point into a triangle, both sides a 4.

As the Pythagorean theorem goes, a^2+b^2=c^2

4^2+4^2=

16+16=

32

The square root of 32 is about 5.7

The distance between the points is about 5.7 units

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Answer:

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Step-by-step explanation:

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2 years ago
Sharon wants to start a savings account with the money she earns selling scented candles. She already has $50 and would like to
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Answer:

She must sell as least 20 candles

Step-by-step explanation:

Sharon has 50 dollars

She makes 2 dollars per candle

Money in 50+2c

She needs at least 90

90≤ 50+2c

We need to solve this inequality

Subtract 50 from each side

90-50≤ 50-50+2c

40 ≤ 2c

Divide by 2

40/2 ≤ 2c/2

20 ≤ c

She must sell as least 20 candles

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The answer is 50 because you have to add it
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