The number of pieces of popcorn in a large movie theater popcorn bucket is normally distributed, with a mean of 1610 and a stand
ard deviation of 10. Approximately what percentage of buckets contain between 1600 and 1620 pieces of popcorn?
A. approximately 68%
B. approximately 75%
C. approximately 95%
D. approximately 99.7%
A. approximately 68%
B. approximately 75%
C. approximately 95%
D. approximately 99.7%
2 answers:
Answer:
A. Approximately 68%
Step-by-step explanation:
Number of pieces of popcorn in a bucket is normally distributed.
Mean = μ = 1610
Standard deviation = б = 10
We know that in normal distribution, approximately 34% of bags will fall with in 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 about 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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Answer:
13.86%
Step-by-step explanation:
Data provided in the question:
Forecasted value bond portfolio one year ahead = $105 million
Expected value to be received = $10,000,000
Worth of bond portfolio today = $101 million
Now,
The Forecasted return is calculated as;
= [(Coupon + closing value - opening value) ÷ (Opening value)] × 100%
on substituting the respective values, we get
Forecasted return =
or
Forecasted return = 0.1386 × 100%
or
Forecasted return = 13.86%