Ana has gotten very good at playing the ukulele and would like to open her own music class. She has been saving all her money for a year and has accumulated $1,340 to buy 20 ukuleles and be able to open her own music class. She has decided to buy the higher end ukuleles manufactured by Lanakai. What is the probability that the average price of the ukulele purchase by Ana will be at most 67 dollars (this is equivalent to total price for 20 ukuleles being at most $1,340, which is the amount of money Ana has saved)?

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Answer question 6.c

Assume that the only 2 manufacturers of ukuleles are Makala and Lanakai.
• The prices of ukuleles manufactured by Makala are normally distributed with mean 45 dollars and standard deviation 10 dollars.
• The prices of ukuleles manufactured by Lanakai are normally distributed with mean 65 dollars and standard deviation 5 dollars.
Ana is learning to play the ukulele at school and is saving her money to buy a higher end Lanakai ukulele. She receives a ukulele for her birthday as a
present and the receipt was included. The ukulele does not have a manufacturer label so she does not know if it is manufactured by Makala or Lanakai,
so she will have to determine the manufacturer based on price, that is, to test the competing hypotheses
Họ: The ukulele is manufactured by Makala
versus
Hạ: The ukulele is manufactured by Lanakai
She will use the following rule:
If the price of the ukulele is 57 dollars or more, she will decide that it was manufactured by Lanakai (Ha),
but if the price of the ukulele is less than 57 dollars, she will decide that it was manufactured by Makala (Ho).
Transcribed Image Text:Assume that the only 2 manufacturers of ukuleles are Makala and Lanakai. • The prices of ukuleles manufactured by Makala are normally distributed with mean 45 dollars and standard deviation 10 dollars. • The prices of ukuleles manufactured by Lanakai are normally distributed with mean 65 dollars and standard deviation 5 dollars. Ana is learning to play the ukulele at school and is saving her money to buy a higher end Lanakai ukulele. She receives a ukulele for her birthday as a present and the receipt was included. The ukulele does not have a manufacturer label so she does not know if it is manufactured by Makala or Lanakai, so she will have to determine the manufacturer based on price, that is, to test the competing hypotheses Họ: The ukulele is manufactured by Makala versus Hạ: The ukulele is manufactured by Lanakai She will use the following rule: If the price of the ukulele is 57 dollars or more, she will decide that it was manufactured by Lanakai (Ha), but if the price of the ukulele is less than 57 dollars, she will decide that it was manufactured by Makala (Ho).
6.c
Ana has gotten very good at playing the ukulele and would like to open her own music class. She has been saving all her money for a year and has
accumulated $1,340 to buy 20 ukuleles and be able to open her own music class. She has decided to buy the higher end ukuleles manufactured by
Lanakai. What is the probability that the average price of the ukulele purchase by Ana will be at most 67 dollars (this is equivalent to total price for 20
ukuleles being at most $1,340, which is the amount of money Ana has saved)?
0.8849
0.1151
0.9452
0.0548
0.9500
0.05
0.9633
0.0367
0.6554
0.3446
0.9000
0.10
Transcribed Image Text:6.c Ana has gotten very good at playing the ukulele and would like to open her own music class. She has been saving all her money for a year and has accumulated $1,340 to buy 20 ukuleles and be able to open her own music class. She has decided to buy the higher end ukuleles manufactured by Lanakai. What is the probability that the average price of the ukulele purchase by Ana will be at most 67 dollars (this is equivalent to total price for 20 ukuleles being at most $1,340, which is the amount of money Ana has saved)? 0.8849 0.1151 0.9452 0.0548 0.9500 0.05 0.9633 0.0367 0.6554 0.3446 0.9000 0.10
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