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solniwko [45]
3 years ago
15

Given that an American is a male, what is the probability that he prefers name-brand milk? b. Given that an American is a female

, what is the probability that she prefers name-brand milk? c. Is preference independent of gender? Explain

Mathematics
1 answer:
Evgesh-ka [11]3 years ago
3 0

Answer:

a) 0.280

b) 0.300

c) No, preference is not independent of gender. Since the P(N) (0.29) is not equal to P(N|M) (0.28) and/or P(N|F) (0.30), the preference and gender are not completely, statistically independent. It's very close though.

Step-by-step explanation:

Let the probability that the somebody surveyed is a male be P(M)

Let the probability that somebody surveyed is female be P(F)

Let the probability that somebody surveyed picked the name-brand milk be P(N)

Let the probability that somebody surveyed picked the store-brand milk be P(St)

Let the probability that somebody surveyed picked the something else be P(So)

a) Given that an American is a male, what is the probability that he prefers name-brand milk = P(N|M) = 319/1138 = 0.280

b) Given that an American is a female, what is the probability that she prefers name-brand milk = P(N|F) = 341/1138 = 0.300

c) To investigate if the preference and gender are independent or not, we need the P(N)

P(N) = probability that an average an Average American (male or female) will prefer a nam-brand milk = 660/2276 = 0.290.

Since the P(N) (0.29) is not equal to P(N|M) (0.28) and/or P(N|F) (0.30), the preference and gender are not statistically independent. It's very close though.

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Question 14 (1 point)
labwork [276]

Answer:

Step-by-step explanation:

I don't think it really does grow by a constant rate. As he puts money in, the amount he puts in becomes less significant to the total.

Suppose he starts at 100 dollars.

After week one, he puts in 100 + 15 = 115 dollars.

The 15 dollars represents an increase of  15/100

After the second week, he puts in another 15 dollars. He has 115 in there already.

(15/115) * 100% = 13.04%

After the third week, he puts in another 15 dollars. (15/130 ) * 100% = 11.53

And so one

4 0
3 years ago
An automated egg carton loader has a 1% probability of cracking an egg, and a customer will complain if more than one egg per do
vaieri [72.5K]

Answer:

a) Binomial distribution B(n=12,p=0.01)

b) P=0.007

c) P=0.999924

d) P=0.366

Step-by-step explanation:

a) The distribution of cracked eggs per dozen should be a binomial distribution B(12,0.01), as it can model 12 independent events.

b) To calculate the probability of having a carton of dozen eggs with more than one cracked egg, we will first calculate the probabilities of having zero or one cracked egg.

P(k=0)=\binom{12}{0}p^0(1-p)^{12}=1*1*0.99^{12}=1*0.886=0.886\\\\P(k=1)=\binom{12}{1}p^1(1-p)^{11}=12*0.01*0.99^{11}=12*0.01*0.895=0.107

Then,

P(k>1)=1-(P(k=0)+P(k=1))=1-(0.886+0.107)=1-0.993=0.007

c) In this case, the distribution is B(1200,0.01)

P(k=0)=\binom{1200}{0}p^0(1-p)^{12}=1*1*0.99^{1200}=1* 0.000006 = 0.000006 \\\\ P(k=1)=\binom{1200}{1}p^1(1-p)^{1199}=1200*0.01*0.99^{1199}=1200*0.01* 0.000006 \\\\P(k=1)= 0.00007\\\\\\P(k\leq1)=0.000006+0.000070=0.000076\\\\\\P(k>1)=1-P(k\leq 1)=1-0.000076=0.999924

d) In this case, the distribution is B(100,0.01)

We can calculate this probability as the probability of having 0 cracked eggs in a batch of 100 eggs.

P(k=0)=\binom{100}{0}p^0(1-p)^{100}=0.99^{100}=0.366

5 0
3 years ago
Using the Slope-Intercept form, find the equation of a line that has a slope of 3 and y - intercept (2)
RideAnS [48]

Answer:

y = 3x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3 and c = 2 , then

y = 3x + 2 ← equation of line

5 0
3 years ago
How many different arrangements of 5 letters can be made from the 26 letters of the alphabet?
VikaD [51]
Answer: P(26,5).

That is all the possible combinations of 5 letters made out from 26 letters.

That is 26! / [ 5! ( 26 - 5)! ] = 26! / [5! 21! ] = 26*25*24*23*22*21! / [ 5! 21!] =

= 26*25*24*23*22 / [5*4*3*2*1] = 65,780 arrangements.


5 0
3 years ago
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Natasha_Volkova [10]
The best answer is c
6 0
3 years ago
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