Do the values in the table represent a proportional relationship?
1 answer:
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Answer:
0.3594 = 35.94% probability that greater than 96 out of 153 DVDs will work correctly.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
Probability that greater than 96 out of 153 DVDs will work correctly.
97 or more DVDs, which is 1 subtracted by the pvalue of Z when X = 97. So
has a pvalue of 0.6406
1 - 0.6406 = 0.3594
0.3594 = 35.94% probability that greater than 96 out of 153 DVDs will work correctly.
Answer:
Profit = $18.8 per meal
Step-by-step explanation:
Chef ordered beef = 4 pounds
Cost of beef = $3.25 per pound
Total cost of beef = 4 × 3.25 = $13
Amount of potatoes ordered = 6 pounds
Cost of potatoes = $1.96 per pound
Total cost of potatoes = 6 × 1.96
= $11.76
Amount of carrots ordered = 5 pounds
Cost of carrots = $1.81 per pound
Total cost of carrots = 5 × 1.81 = $9.05
Total amount of beef, potatoes and carrots = $13 + $11.76 + $9.05
= $33.81
Number of meals prepared with material purchased = 28
Per meal cost = = $1.2075
Selling price of one meal = $20
Profit per meal = Selling price - Cost price
= 20 - 1.2075
= 18.7925
≈ $18.8
Therefore, he will make $18.8 for each meal.