Question

The number of pieces of popcorn in a large movie theatre popcorn bucket is normally distributed, with a mean of 1610 and a standard deviation of 10. Approximately what percentage of buckets contain between 1600 and 1620 pieces of popcorn?

Approximately 68%
Approximately 75%
Approximately 95%
Approximately 99.7%

Answers

  2. Answer:
    A. Approximately 68%
    Step-by-step explanation:
    The number of pieces of popcorn in a bucket is normally distributed.
    Mean = μ = 1610
    Standard deviation = б = 10
    We know that in a normal distribution, approximately 34% of bags will fall within one standard deviation on one side. On both sides within the range of 1 standard deviation, 34 + 34 = 68 % of bags will fall.
    A table of normal distribution of the mean is attached for better understanding.
    Our range is:
    1600 to 1620
    1610 – 10 to 1610 + 10
    μ ± б
    mean ± 1 standard deviation
    Our range is within 1 standard deviation. Hence, Approximately 68% of buckets contain between 1600 and 1620 pieces of popcorn.

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