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Natalka [10]
2 years ago
11

Erin uses a spinner divided into four equal sections to decide which drink she’ll have with her lunch. The sections represent wa

ter, milk, lemonade, and tea. If she spins the spinner three days in a row, what is the probability that she drinks lemonade one day, tea one day, and water one day? Complete the steps below to find the sample space and solve the problem. PART A - Create a list of all the possible outcomes for three days of drink selections. Use the abbreviations W, M, T, and L to represent water, milk, tea, and lemonade. PART B - Based on the list you created in part A, how many possible outcomes are there? PART C - What is the probability that Erin drinks lemonade one day, tea one day, and water one day? PART D - What is the probability that Erin drinks water two days and lemonade one day?
Mathematics
1 answer:
lys-0071 [83]2 years ago
8 0

Answer:

Part A

W W W M W W T W W L W W

W W M M W M T W M L W M

W W T M W T T W T L W T

W W L M W L T W L L W L

W M W M M W T M W L M W

W M M M M M T M M L M M

W M T M M T T M T L M T

W M L M M L T M L L M L

W T W M T W T T W L T W

W T M M T M T T M L T M

W T T M T T T T T L T T

W T L M T L T T L L T L

W L W M L W T L W L L W

W L M M L M T L M L L M

W L T M L T T L T L L T

W L L M L L T L L L L L

Part B

There are 64 possible outcomes. The sample size is 64.

Part C

To find the probability that Erin drinks lemonade one day, tea one day, and water one day, consider all the cases in which L, T, and W occur one time. Because the order doesn't matter in this scenario, these six outcomes from the list represent the desired event: W T L, T W L, T L W, W L T, L W T, and L T W.

The size of the sample space is 64. So, the probability that Erin drinks lemonade one day, tea one day, and water one day is 3/32.

Part D

To find the probability that Erin drinks water on two days and lemonade one day, we consider all the cases in which two Ws and one L occur. Because the order doesn't matter in this scenario, these three outcomes from the list represent the event: W W L, W L W, and L W W.

The size of the sample space is 64. So, the probability that Erin drinks water two days and lemonade one day is 3/64

Step-by-step explanation:

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Newborn babies: A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights
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b) 715

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Step-by-step explanation:

According to the Question,

  • Given that,  A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 732 babies born in New York. The mean weight was 3311 grams with a standard deviation of 860 grams

  • Since the distribution is approximately bell-shaped, we can use the normal distribution and calculate the Z scores for each scenario.

Z = (x - mean)/standard deviation

Now,

For x = 4171,  Z = (4171 - 3311)/860 = 1  

  • P(Z < 1) using Z table for areas for the standard normal distribution, you will get 0.8413.

Next, multiply that by the sample size of 732.

  • Therefore 732(0.8413) = 615.8316, so approximately 615 will weigh less than 4171  

 

  • For part b, use the same method except x is now 1591.    

Z = (1581 - 3311)/860 = -2    

  • P(Z > -2) , using the Z table is 1 - 0.0228 = 0.9772 . Now 732(0.9772) = 715.3104, so approximately 715 will weigh more than 1591.

 

  • For part c, we now need to get two Z scores, one for 3311 and another for 5031.

Z1 = (3311 - 3311)/860 = 0

Z2 = (5031 - 3311)/860= 2  

P(0 ≤ Z ≤ 2) = 0.9772 - 0.5000 = 0.4772

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