I need some help with this problem.

Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and

sergij07 [2.7K]

Answer:

a) sample size is 40

Step-by-step explanation:

(a)

$\sigma=4$ minutes

Margin of error, E is 75 seconds E=75/60= 1.25 minutes.

The level of significance $\alpha= 0.05$ for 95% level of significance

For 95% confidence interval $z_{\frac{\alpha}{2}}=1.96$ from standard deviation table

Sample size required, n

$n=\left (\frac{z_{\frac{\alpha}{2}}\cdot \sigma}{E} \right )^{2}=\left (\frac{1.96\cdot4}{75/60} \right )^{2}=39.337984$

Rounding off, n=40

Sample size =40

Keywords:

95% confidence, sample size, Wall Street Journal

3 0

3 years ago

Use benchmarks to estimate 16.8-5.94

Sunny_sXe [5.5K]

The estimated answer is 11. First you round 16.8 to 17 because the decimal is above 5. Then you round 5.94 to 6 because the first decimal place is greater than 5. Lastly you subtract 17 minus 5 to get 11.

7 0

3 years ago

2 Probability and Stats questions!!

mart [117]

1) To find the confidence interval
the sample mean x = 38 σ = 9; n = 85;
The confidence level is 95% (CL = 0.95) CL = 0.95
so α = 1 – CL = 0.05
α/2 = 0.025 Z(α/2) = z0.025
The area to the right of Z0.025 is 0.025 and the area to the left of Z0.025 is 1 – 0.025 = 0.975
Z(α/2) = z0.025 = 1.645 This can be found using a computer, or using a probability table for the standard normal distribution.
EBM = (1.645)*(9)/(85^0.5)=1.6058 x - EBM = 38 – 1.6058 = 36.3941 x + EBM = 38 + 1.6058 = 39.6058
The 95% confidence interval is (36.3941, 39.6058).
The answer is the letter D
The value of 40.2 is within the 95% confidence interval for the mean of the sample

2) To find the confidence interval 
the sample mean x = 76 σ = 20; n = 102; 
The confidence level is 95% (CL = 0.95) CL = 0.95
so α = 1 – CL = 0.05
α/2 = 0.025 Z(α/2) = z0.025
The area to the right of Z0.025 is 0.025 and the area to the left of Z0.025 is 1 – 0.025 = 0.975
Z(α/2) = z0.025 = 1.645 This can be found using a computer, or using a probability table for the standard normal distribution.
EBM = (1.645)*(20)/(102^0.5)=3.2575 x - EBM = 76 – 3.2575 = 72.7424 x + EBM = 76 + 3.2575 = 79.2575 
The 95% confidence interval is (72.7424 ,79.2575).
The answer is the letter A and the letter D
The value of 71.8 and 79.8 are outside the 95% confidence interval for the mean of the sample

5 0

3 years ago

A certain kind of sheet metal has, on average, 3 defects per 18 square feet. Assuming a Poisson distribution, find the probabili

Fofino [41]

Answer:

75.8% probability that a 31 square foot metal sheet has at least 4 defects.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$