3+4x+x^2 = y Given x = 1
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a (i) The number of standard size is 288 eggs
a (ii) The number of medium size is 1,476 eggs
a (iii) The number of large size is 36 eggs
b (i) The expected profit made from selling the standard size is Gh¢43.2
b (ii) The expected profit made from selling the medium size is Gh¢516.6
b (iii) The expected profit made from selling the large size is Gh¢16.2
The given parameters:
the mean of the distribution, m = 0.06 kg
standard deviation (std) of the distribution, d = 0.009 kg
number of the samples, n = 1800 eggs
(i) Find the position of "less than 0.052 kg (standard size)":
- 1 standard deviation below the mean = m - d
- m - d = 0.06 kg - 0.009 kg = 0.051 kg
(<em>the </em><em>standard size</em><em> is 1 standard deviation below the mean</em>)
- less than 1 standard deviation below the mean in a normal distribution is equal to 16% of the data samples
- Number of standard size = 0.16 x 1800 = 288 eggs
(ii) Find the position of "Between 0.052 kg and 0.075kg (medium size)":
- 0.052 kg is 1 standard deviation below the mean
- 2 standard deviation above the mean = m + 2d
- m + 2d = 0.06 + 2(0.009) = 0.078 kg
(<em>the </em><em>medium size</em><em> is between 1 std below the mean and 2 std above the mean</em>)
- Between 1 std below the mean and 2 std above the mean in a normal distribution = (68 + 14)% = 82%
- Number of medium size = 0.82 x 1800 = 1,476 eggs
(iii) Find the position of "Greater than 0.075 kg (large size)":
- 0.078 kg is 2 standard deviation below the mean
- greater than 2 std above the mean in a normal distribution = 2 % of the data samples
- Number of large size = 0.02 x 1800 = 36 eggs
<u>Check:</u> <em>288 eggs + 1476 eggs + 36 eggs = 1,800 eggs</em>
(b) the cost of production of an egg = Gh¢0.45
the selling price of the standard size = Gh¢0.60
the selling price of the medium size = Gh¢0.80
the selling price of the large size = Gh¢0.95
(i) The expected profit made from selling the standard size:
Profit = total revenue - cost of production
Profit = 288(0.6) - 288(0.45) = Gh¢43.2
(ii) The expected profit made from selling the medium size:
Profit = total revenue - cost of production
Profit = 1476(0.8) - 1476(0.45) = Gh¢516.6
(iii) The expected profit made from selling the large size:
Profit = total revenue - cost of production
Profit = 36(0.9) - 36(0.45) = Gh¢16.2
Learn more here: brainly.com/question/22520030
Answer: 0.9617
Step-by-step explanation:
Given : The proportion of adults use their phones in meetings or classes : p=0.57
Number of adults randomly selected : n= 9
Let x be the random variable that represents the number of adults use their phones in meetings or classes.
By using binomial probability formula, to find the probability of getting success in x trials.
The probability that at least 3 of them use their smartphones in meetings or classes will be :-
Hence, the required probability is 0.9617 .
Answer:
a) Therefore 92.64% of customers receive the service for half-price.
b) Therefore it would take 8.52 minutes
Step-by-step explanation:
Given that ime required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution with:
mean (μ) = 15 minutes
Standard deviation (σ) = 3.5 minutes
a) The z score is given by the equation:
Since the service will take no longer than 20 minutes,
Using the probability table to get the probability of the z score
percent of customers receive the service for half-price = P(X < 20) = P(z < 1.43) = 0.9236 = 92.64%
Therefore 92.64% of customers receive the service for half-price.
b) Since the probability is 3% = 0.03, this corresponds with a z score of -1.88
Therefore:
Therefore it would take 8.52 minutes