MATHEMATICS COLLEGE

The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.Requried:
a. What is the probabilty that a random sample of n = 40 oil changes results in a sample mean time less than 15 minutes?
b. Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there
would be a 10% chance of the mean oil-change time being at or below what value? This will be the goal established by the manager.

Answers

Answer 1

Answer:

(a) Probability that a random sample of n = 45 oil changes results in a sample mean time < 10 minutes i=0.0001.

(b) The mean oil-change time is 15.55 minutes.

Step-by-step explanation:

Let us denote the sample mean time as x

From the Then x = mean time = 16.2 minutes

The given standard deviation = 3.4 minutes

The value of n sample size = 45

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

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Suppose that 30% of all students who have to buy a text for a particular course want a new copy (the successes!), whereas the other 70% want a used copy. Consider randomly selecting 15 purchasers.The bookstore has 10 new copies and 10 used copies in stock.
If 15 people come in one by one to purchase this text, what is the probability that all 15 will get the type of book they want from current stock?

Answers

Answer:

The probability that all 15 will get the type of book they want from current stock is 0.4838.

Step-by-step explanation:

Denote the random variable Xas the number of students who want to buy new copy.

The probability of a student wanting to buy a new copy is, P (X) = p = 0.30.

A random sample of n = 15 students is selected.

The random variable X follows a Binomial distribution.

The probability function of a Binomial distribution is:

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

It is provided that the bookstore has 10 new copies and 10 used copies in stock.

All the 15 students get their desired copy, then this can happen if at most 10 want to buy new copy and at least 5 wants to buy used copy.

Compute the probability of (5 ≤ X ≤ 10) as follows:

P (5 ≤ X ≤ 10) = P (X = 5) + P (X = 6) + P (X = 7) + P (X = 8) + P (X = 9) + P (X = 10)

$={15\choose 5}(0.30)^(5)(1-0.30)^(15-5)+{15\choose 6}(0.30)^(6)(1-0.30)^(15-6)\n+{15\choose 7}(0.30)^(7)(1-0.30)^(15-7)+{15\choose 8}(0.30)^(8)(1-0.30)^(15-8)\n+{15\choose 9}(0.30)^(9)(1-0.30)^(15-9)+{15\choose 10}(0.30)^(10)(1-0.30)^(15-10)\n=0.2061+0.1472+0.0811+0.0348+0.0116+0.0030\n=0.4838$

Thus, the probability that all 15 will get the type of book they want from current stock is 0.4838.

What is the inverse of the function f(x)=2x+1?

Answers

Answer:

see the attachment

Step-by-step explanation:

You can find the inverse by swapping the variables and solving for y.

y = f(x) . . . . . original function

x = f(y) . . . . . variables swapped

x = 2y +1

x -1 = 2y . . . subtract 1

(x-1)/2 = y . . . divide by 2

y = (1/2)x -1/2 . . . expand

If the inverse function is named h(x), then it is ...

h(x) = x/2 -1/2

Answer:

Option 1.

Step-by-step explanation:

$y=2x+1$

$x=2y+1$

$x-1=2y$

$(x-1)/(2) = (2y)/(2)$

$(x-1)/(2) = y$

$(1)/(2)x -(1)/(2) = y$

. Write 3.476 x 1011 in standard notation.

Answers

Answer: 347,600,000,000

Step-by-step explanation: You have to move the decimal 11 places. After you move it behind the 6 to get the number 3,476, you have to move it 8 more times because 11-3 is 8. So you add 8 zeros

Determine whether the following examples are discrete or continuous data sets. (a) The length of time it takes to fill up your gas tank. (b) The number of students applying to graduate schools. (c) The number of voters who vote Democratic. (d) The number of customers waiting in line at the grocery store

Answers

(a) The length of time it takes to fill up your gas tank - Continuous

(b) The number of students applying to graduate schools - Continuous

(d) The number of customers waiting at the grocery store-Discrete

What is the difference between continuous and discrete data?

Continuous data can have an infinite range of values while Discrete data can take some certain values only.

Let us consider the given examples

a) The length of time it takes to fill up your gas tank.

In this case, the time duration can be of a wide range. Time taken while filling up a gas tank can take many values. So it is an example of continuous data.

b) The number of students applying to graduate schools.

In this case, the number of students applying to graduate schools can be of a wide range. it can be n number of values. So it is an example of continuous data.

c)The number of voters who vote Democratic.

The number of voters who vote can be of a certain value. Hence, this is an example of discrete data.

d)The number of customers waiting in line at the grocery store.

The number of customers waiting in line at the grocery store can be of a certain value. Hence, this is an example of discrete data.

Therefore, we can say that

(a) The length of time it takes to fill up your gas tank - Continuous

(b) The number of students applying to graduate schools - Continuous

(d) The number of customers waiting at the grocery store-Discrete

To get more about continuous and discrete data refer to the link,

brainly.com/question/2931136

Answer:

(a) The length of time it takes to fill up your gas tank - CONTINUOUS

(b) The number of students applying to graduate schools - CONTINUOUS

(d) The number of customers waiting in line at the grocery store - DISCRETE

Step-by-step explanation:

To determine either the set of data are discrete or continuous, let consider their characteristics.

CONTINUOUS

continuous data is quantitative data, It can be measured, it has an infinite values within selected range.

DISCRETE

Discrete data is counted, it can only take certain values.

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