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2 answers:
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Answer:
(a) The probability the salesperson will make exactly two sales in a day is 0.1488.
(b) The probability the salesperson will make at least two sales in a day is 0.1869.
(c) The percentage of days the salesperson does not makes a sale is 43.05%.
(d) The expected number of sales per day is 0.80.
Step-by-step explanation:
Let <em>X</em> = number of sales made by the salesperson.
The probability that a potential customer makes a purchase is 0.10.
The salesperson contacts <em>n</em> = 8 potential customers per day.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.
The probability mass function of <em>X</em> is:
(a)
Compute the probability the salesperson will make exactly two sales in a day as follows:
Thus, the probability the salesperson will make exactly two sales in a day is 0.1488.
(b)
Compute the probability the salesperson will make at least two sales in a day as follows:
P (X ≥ 2) = 1 - P (X < 2)
= 1 - P (X = 0) - P (X = 1)
Thus, the probability the salesperson will make at least two sales in a day is 0.1869.
(c)
Compute the probability that a salesperson does not makes a sale is:
The percentage of days the salesperson does not makes a sale is,
0.4305 × 100 = 43.05%
Thus, the percentage of days the salesperson does not makes a sale is 43.05%.
(d)
Compute the expected number of sales per day as follows:
Thus, the expected number of sales per day is 0.80.
Answer:
y = 11.84x - 32.71
Step-by-step explanation:
Here, the given data points,
(−3,−70),(−1,−42),(1,−21),(2,−9),(4,14),
Let x represents the input value and y represents the output value,
So, the table that represents the given situation is,
x -3 -1 1 2 4
y -70 -42 -21 -9 14
By the above table,
Let the equation of the line is,
y = bx + a
Where,
n = number of data points = 5,
By substituting the values we get,
a = - 32.70547945 ≈ - 32.71,
b = 11.84246575 ≈ 11.84,
Hence, the equation of line would be,
y = 11.84x - 32.71