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Vedmedyk [2.9K]

3 years ago

15

Question 12 The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of and

a standard deviation of . Find the probability that the mean GPA of a random sample of students selected from this university is or higher.

1 answer:

andreev551 [17]3 years ago

8 0

Complete question :

The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of 3.02 and a standard deviation of .29.Find the probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.

Answer:

0.10868

Step-by-step explanation:

Given that :

Mean (m) = 3.02

Standard deviation (s) = 0.29

Sample size (n) = 20

Probability of 3.10 GPA or higher

P(x ≥ 3.10)

Applying the relation to obtain the standardized score (Z) :

Z = (x - m) / s /√n

Z = (3.10 - 3.02) / 0.29 / √20

Z = 0.08 / 0.0648459

Z = 1.2336940

p(Z ≥ 1.2336) = 0.10868 ( Z probability calculator)

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Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining wh

Molodets [167]

Answer:

(A) The mean for the differences is 2.0.

(B) The test statistic is 1.617.

(C) At 90% confidence the null hypothesis should not be rejected.

Step-by-step explanation:

We are given that a random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.

The following data (in miles per gallon) show the results of the test;

Driver Manufacturer A Manufacturer B

1 32 28

2 27 22

3 26 27

4 26 24

5 25 24

6 29 25

7 31 28

8 25 27

Let $\mu_1$ = mean MPG for the fuel efficiency of Manufacturer A brand

$\mu_2$ = mean MPG for the fuel efficiency of Manufacturer B brand

SO, Null Hypothesis, $H_0$ : $\mu_1-\mu_2=0$ or $\mu_1= \mu_2$ {means that there is a not any significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles}

Alternate Hypothesis, $H_A$ : $\mu_1-\mu_2\neq 0$ or $\mu_1\neq \mu_2$ {means that there is a significant difference in the mean MPG (miles per gallon) for the fuel efficiency of these two brands of automobiles}

The test statistics that will be used here is <u>Two-sample t test statistics</u> as we don't know about the population standard deviations;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t__n__1+_n__2-2$

where, $\bar X_1$ = sample mean MPG for manufacturer A = $\frac{\sum X_A}{n_A}$ = 27.625

$\bar X_2$ = sample mean MPG for manufacturer B = $\frac{\sum X_B}{n_B}$ = 25.625

$s_1$ = sample standard deviation for manufacturer A = $\sqrt{\frac{\sum (X_A-\bar X_A)^{2} }{n_A-1} }$ = 2.72

$s_2$ = sample standard deviation manufacturer B = $\sqrt{\frac{\sum (X_B-\bar X_B)^{2} }{n_B-1} }$ = 2.20

$n_1$ = sample of cars selected from manufacturer A = 8

$n_2$ = sample of cars selected from manufacturer B = 8

Also, $s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(8-1)\times 2.72^{2}+(8-1)\times 2.20^{2} }{8+8-2} }$ = 2.474

(A) The mean for the differences is = 27.625 - 25.625 = 2

(B) <u><em>The test statistics</em></u> = $\frac{(27.625-25.625)-(0)}{2.474 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }$ ~ $t_1_4$

= 1.617

(C) Now at 10% significance level, the t table gives critical values between -1.761 and 1.761 at 14 degree of freedom for two-tailed test. Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that there is a not any significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.

5 0

3 years ago

Work out the area of ABCD.

lapo4ka [179]

Answer:

efghijklmnopqrstuvwxyz, thank me later

7 0

2 years ago

A young sumo wrestler decided to go on a diet to gain weight rapidly. He gained weight at a rate of 5.5kg a month. After 11 mont

kondaur [170]

Answer:

$W(t)=5.5t+79.5$ .

Step-by-step explanation:

Please consider the complete question.

A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He gained weight at a rate of 5.5 kilograms per month. After 11 months, he weighed 140 kilograms. Let W(t) denote the sumo wrestler's weight W(measured in kilograms) as a function of time t (measured in months).

Since wrestler gained weight at a rate of 5.5 kilograms per month, so slope of line be 5.5.

Now, we will use point-slope form of equation as:

$y-y_1=m(x-x_1)$ , where,

m = Slope

$(x_1,y_1)$ = Given point on the line.

Upon substituting coordinates of point (11,140) in above formula, we will get:

$y-140=5.5(x-11)$

$y-140=5.5x-60.5$

$y-140+140=5.5x-60.5+140$

$y=5.5x+79.5$

Therefore, our required function would be $W(t)=5.5t+79.5$ .

3 0

3 years ago

Triangles H J K and L M N are congruent. Triangle H J K is rotated about point H to form triangle L N M. Triangle L M N is highe

Alex

Answer:

a rotation about point H

Step-by-step explanation:

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7 0

3 years ago

Read 2 more answers

A) Factorise 2x² - 9x - 5 (x-5)(2x+1) (2) <br>b) Hence, simplify fully 2x^2- 9x - 5 3x – 15x (2)

Lyrx [107]

Answer:

Step-by-step explanation:

<u><em>b).</em></u>

2x² - 9x - 5 = ( x - 5 )( 2x + 1 )

3x² - 15x = 3x ( x - 5 )

$\frac{(x-5)(2x+1)}{3x(x-5)}$ = $\frac{2x+1}{3x}$

8 0

2 years ago