Suppose that 56% of children prefer whole-grain snacks to non-whole-grain snacks. A random sample of 80 children is taken. (a) Verify that we can use the Normal distribution to compute probabilities about the sample proportions of children who prefer whole-grain snacks by checking the assumptions: 1. Independence Assumption, checked by the Randomization Condition: 2. Sample Size Assumption, checked by the Success/Failure Condition: (b) What are the centre and spread of the normal distribution of p? E(P) = SD(P) = (c) What is the probability that less than 40 of the children prefer whole-grain snacks? Draw the diagram for this probability. (d) What is the probability that between 32 and 52 of the children prefer whole-grain snacks? Draw the diagram for this probability.

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Question 4:
Suppose that 56% of children prefer whole-grain snacks to non-whole-grain snacks. A random
sample of 80 children is taken.
(a) Verify that we can use the Normal distribution to compute probabilities about the sample
proportions of children who prefer whole-grain snacks by checking the assumptions:
1. Independence Assumption, checked by the Randomization Condition:
2. Sample Size Assumption, checked by the Success/Failure Condition:
(b) What are the centre and spread of the normal distribution of p?
E(f) =
SD(P)
(c) What is the probability that less than 40 of the children prefer whole-grain snacks? Draw
the diagram for this probability.
(d) What is the probability that between 32 and 52 of the children prefer whole-grain snacks?
Draw the diagram for this probability.
Transcribed Image Text:Question 4: Suppose that 56% of children prefer whole-grain snacks to non-whole-grain snacks. A random sample of 80 children is taken. (a) Verify that we can use the Normal distribution to compute probabilities about the sample proportions of children who prefer whole-grain snacks by checking the assumptions: 1. Independence Assumption, checked by the Randomization Condition: 2. Sample Size Assumption, checked by the Success/Failure Condition: (b) What are the centre and spread of the normal distribution of p? E(f) = SD(P) (c) What is the probability that less than 40 of the children prefer whole-grain snacks? Draw the diagram for this probability. (d) What is the probability that between 32 and 52 of the children prefer whole-grain snacks? Draw the diagram for this probability.
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