A manufacturer of children's vitamins claims that its vitamins are mixed so that each batch has exactly the following percentages of each color: 10 % green, 30% yellow, 30 % red, and 30 % orange. To test the claim that these percentages are incorrect, 100 bottles of vitamins were sampled and the colors of the vitamins were tallied. The results are listed in the following table. At a = 0.025, determine whether there is sufficient evidence to conclude that the percentages stated by the vitamin manufacturer are incorrect. Children's Vitamins Green Yellow Red Orange Number 590 1765 1717 1615 Copy Data Step 2 of 4: Calculate the expected value for the number of vitamins that are orange. Round your answer to three decimal places, if necessary.

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A manufacturer of children's vitamins claims that its vitamins are mixed so that each batch has exactly the following percentages of each color:
10 % green, 30 % yellow, 30 % red, and 30 % orange. To test the claim that these percentages are incorrect, 100 bottles of vitamins
were sampled and the colors of the vitamins were tallied. The results are listed in the following table. At a = 0.025, determine whether there
is sufficient evidence to conclude that the percentages stated by the vitamin manufacturer are incorrect.
Children's Vitamins
Green
Yellow
Red
Orange
Number
590
1765
1717
1615
Copy Data
Step 2 of 4: Calculate the expected value for the number of vitamins that are orange. Round your answer to three decimal places, if necessary.
Transcribed Image Text:A manufacturer of children's vitamins claims that its vitamins are mixed so that each batch has exactly the following percentages of each color: 10 % green, 30 % yellow, 30 % red, and 30 % orange. To test the claim that these percentages are incorrect, 100 bottles of vitamins were sampled and the colors of the vitamins were tallied. The results are listed in the following table. At a = 0.025, determine whether there is sufficient evidence to conclude that the percentages stated by the vitamin manufacturer are incorrect. Children's Vitamins Green Yellow Red Orange Number 590 1765 1717 1615 Copy Data Step 2 of 4: Calculate the expected value for the number of vitamins that are orange. Round your answer to three decimal places, if necessary.
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