The appropriate measure of center to describe the data distribution is the: Mean Median

Because of staffing decisions, managers of the Gibson-Marion Hotel are interested in the variability in the number of rooms occu

olchik [2.2K]

Answer:

a) $s^2 =30^2 =900$

b) $\frac{(19)(30)^2}{30.144} \leq \sigma^2 \leq \frac{(19)(30)^2}{10.117}$

$567.28 \leq \sigma^2 \leq 1690.224$

c) $23.818 \leq \sigma \leq 41.112$

Step-by-step explanation:

Assuming the following question: Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 20 days of operation shows a sample mean of 290 rooms occupied per day and a sample standard deviation of 30 rooms

Part a

For this case the best point of estimate for the population variance would be:

$s^2 =30^2 =900$

Part b

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The degrees of freedom are given by:

$df=n-1=20-1=19$

Since the Confidence is 0.90 or 90%, the significance $\alpha=0.1$ and $\alpha/2 =0.05$ , the critical values for this case are:

$\chi^2_{\alpha/2}=30.144$

$\chi^2_{1- \alpha/2}=10.117$

And replacing into the formula for the interval we got:

$\frac{(19)(30)^2}{30.144} \leq \sigma^2 \leq \frac{(19)(30)^2}{10.117}$

$567.28 \leq \sigma^2 \leq 1690.224$

Part c

Now we just take square root on both sides of the interval and we got:

$23.818 \leq \sigma \leq 41.112$

5 0

3 years ago

$6x + $15 ≤ $70 I have no idea- xd

Delvig [45]

Answer:

x = 9

Step-by-step explanation:

6 × 9 = 54

54 + 15 = 69, which is less than 70.

3 0

2 years ago

Consider the rectangle enlargement. Pls answer the three questions I will mark brainliest!!

Alenkasestr [34]

Answer:

Perimeter of the original Rectangle is

2(4.5+4.3)=2×8.8= 17.6 mm

Side length of the enlarged rectangle is

$\frac{4.5}{4.3} = \frac{24.3}{x} \\ x = \frac{24.3 \times 4.3}{4.5} \\ \boxed{x = 23.22 \: mm}$

Perimeter of the enlarged rectangle

2(24.3+23.22)= 2×47.52= 95.04 mm

7 0

2 years ago

A company makes pens. They sell each pen for $99.

Sindrei [870]

Answer:

a) Profit = 84000

b) at break even number of pens sold = 46

Step-by-step explanation:

Profit = Selling price - Cost price

Total revenue generated = 99 * 1000

Total revenue generated = 99000

Total cost on making the pen = 11 * 1000

Total cost on making the pen = 11000

Total cost including the initial cost = 11000 + 4000

Total cost including the initial cost = 15000

Profit = 99000 - 15000

Profit = 84000

Break even is when the cost are equal to Revenue thus no profit or loss

Revenue = total cost (break even)

9x = 1x + 4000

9x - x = 4000

8x = 4000

x = 500

At breakeven Revenue = 9 * 500

At breakeven Revenue = 4500

since one pen is sold at 99 therefore at break even number of pens sold = 4500/99 = 45.45( to 2 decimal place)

at break even number of pens sold = 46

4 0

2 years ago

Julie was given a new map of New Hampshire to calculate some distances. The scale is 1 inch = 50 miles. How far is Conway from L

Aloiza [94]

Answer:

Conway is 312.50 miles from Littleton

Step-by-step explanation:

Given

$Scale: 1\ in = 50\ mi$

See attachment

Required

Distance between Conway and Littleton

The scale distance between Conway and Littleton is 6.25 inches.

So, the actual distance is calculated as:

$1\ in = 50\ mi$

Multiply both sides by 6.25

$6.25 * 1\ in = 50\ mi * 6.25$

$6.25\ in = 312.50\ mi$

Hence, Conway is 312.50 miles from Littleton

7 0

2 years ago