Let x be a normal random variable with mean 35 and standard deviation 2.

a. Find P(30 < x < 38).

.9270

b. Find P(x > 34).

.6915

c. Find P(x = 36).

0

d. Find the area under the distribution of x to the left of 31.

.0228

Allegiant Airlines charges a mean base fare of $87. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $37 per passenger. Suppose a random sample of 50 passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population standard deviation of total flight cost is known to be $38. Use z-table.

a. What is the population mean cost per flight?

b. What is the probability the sample mean will be within $10 of the population mean cost per flight (to 4 decimals)?

c. What is the probability the sample mean will be within $5 of the population mean cost per flight (to 4 decimals)?

What is the difference between expected payoff under certainty and expected payoff under risk?

Explain the basic decision environment categories

Assume that when adults with smartphones are randomly selected, 39% use them in meetings or classes. If 5 adults smartphone users are randomly selected, find the probability that exactly 2 of them use their smartphones in meetings or classes.

1. Given sample data: 61.2, 61.9, 62.8, 63.1, 64.0, 64.3, 64.9, 65.5, 66.3 and 67.9,
test H₀: m £ 62.89 versus H₁: m > 62.89 at a = 0.05

2. Test H₀: π = 0.25 versus H_A: π ¹ 0.25 with p = 0.33 and n = 100 at alpha = 0.05 and 0.10.

Thirty percent of all customers who enter a store will make a purchase. Suppose 10 customers enter the store, and that they make independent purchasing decisions.

(a) Let X be the number, out of the 10 customers in the store, who will make a purchase. Write the binomial probability density function for this situation.

(b) Use the binomial distribution to calculate the probability exactly 5 customers make a purchase.

(c) Find the probability that 4 or fewer customers make a purchase.

(d) Find the probability that 7 or more customers make a purchase.

Pharmaceutical companies promote their prescription drugs using television advertising. In a survey of 75 randomly sampled television viewers, 12 indicated that they asked their physician about using a prescription drug they saw advertised on TV.

Develop a 90% confidence interval for the proportion of viewers who discussed a drug seen on TV with their physician. (Round your answers to 3 decimal places.)

Is it reasonable to conclude that 26% of the viewers discuss an advertised drug with their physician?

sampling, variables, hypothesis testing, z scores, and standard deviation

If the probability that a certain tennis player will serve an ace is 1/ 6 , what is the probability that he will serve exactly four aces out of six serves? (Assume that the six serves are independent. Round your answer to four decimal places.)

Is there enough evidence to conclude that the average salary at the Company A is LESS than the average salary at the Company B ( α = 0.04)?

The lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 15 days.

In what range would you expect to find the middle 98% of most pregnancies?
Between _____and ____.

If you were to draw samples of size 36 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?
Between ____and _____ .

Enter your answers as numbers. Your answers should be accurate to 1 decimal places.

Please only respond to this question if you can do so accurately and entirely.

For each situation, perform a hypothesis test for the population mean. Be sure to show the null hypothesis H0, the alternative hypothesis H1, the P-level you get from TTest, the result of the test (i.e. reject / do not reject H0) and the conclusion (interpret the result in English).

A Jedi sage would like proof that Jedi trainees have a higher level of midichlorians than non-Jedis. Non-Jedis have a mean midichlorian level of 2500. A random sample of 25 Jedi trainees have a sample mean midichlorian level of 2875, with a sample standard deviation of 1050. Is this adequate evidence at the α = 0.05 level of certainty that Jedi trainees have higher midichlorian levels than non-Jedis?

H0:

H1:

P-level:

Result:

Conclusion:

a politician claims that the mean salary for managers in his State is more than the national mean, $82,000.00. Assume the population is normally distributed and the population deviation is $9500.00. The salaries(in dollars) for a random sample of 30 managers in the state are listed. At a=0.07, is there enough evidence to support the claim?
the dollar amounts are:$73,747.00, $87,299.00, $77,242.00, $72,623.00, $80,753.00, $83,263.00, $96,365.00, $93,988.00, $87,831.00, $97,484.00, $74,216.00, $71,883.00, $83,884.00, $89,409.00, $78,373.00, $75,138.00, $83,274.00, $91,670.00, $92,903.00, $74,575.00, $77,973.00, $73,195.00, $83,379.00, $73,439.00, $95,380.00, $98,473.00, $99,111.00, $71,077.00, $75,251.00, $74,547.00.
I also need the standardized test statistic and the p-value as well

please find the standardized test statistic and the p- value.

Suppose you perform the following multiple regression: Y = B0 + B1X1 + B2X2 + B3X3. You find that X1 and X3 have a near perfect correlation. How would you conclude on the utility of your regression result? This is a problem of multicollinearity which renders the entire regression invalid. This is a problem of multicollinearity which nevertheless does not invalidate the utility of the model as a whole This is NOT a regression problem and inferences made using the model and the respective coefficients remain valid. This is a problem of multicollinearity. However inferences made concerning the individual contribution of the model coefficients remain valid