If 3p + 41 = 24 and q = 3, find p

AlexFokin [52]

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 X = number of sales made by the salesperson.

The probability that a potential customer makes a purchase is 0.10.

The salesperson contacts n = 8 potential customers per day.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

$P(X=x)={8\choose x}0.10^{x}(1-0.10)^{8-x};\ x=0,1,2,3...$

(a)

Compute the probability the salesperson will make exactly two sales in a day as follows:

$P(X=2)={8\choose 2}0.10^{2}(1-0.10)^{8-2}\\=28\times 0.01\times 0.5314\\=0.1488$

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)

$=1-{8\choose 0}0.10^{0}(1-0.10)^{8-0}-{8\choose 1}0.10^{1}(1-0.10)^{8-1}\\=1-0.4305-0.3826\\=0.1869$

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:

$P(X=0)={8\choose 0}0.10^{0}(1-0.10)^{8-0}\\=8\times 1\times 0.4305\\=0.4305$

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:

$E(X)=np=8\times 0.10=0.80$

Thus, the expected number of sales per day is 0.80.

7 0

3 years ago

crimeas [40]

Based on the given parameters, bhe true statements are: the expression has four terms, and the term -40/y is a ratio.

<h3>How to determine the true statements?</h3>

The expression is given as:

6x^3 - 8x^2 - 40/y + 21

The above expression has four terms, and the terms are:

6x^3, - 8x^2,- 40/y and 21

Also, the term -40/y is a ratio

This is so because it is a quotient of two numbers

Hence, the true statements are: the expression has four terms, and the term -40/y is a ratio, based on the given parameters