Find the probability that a simple random sample of 64 protozoa

Subject: Mathematics    / Statistics
Question

Question 1 Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 49 days and a standard deviation of 10.2 days. Find the probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days.

a)0.2000

b)0.0000

c)0.0001

d)0.6880

e)1.0000

f)None of the above

Question 2 What effect does decreasing the sample size have on a distribution of sample means?

a)It will not make any difference

b)It will have more variation

c)It will have less variation

Question 3 In a large population, 84% of the households have cable tv. A simple random sample of 81 households is to be contacted and the sample proportion computed. What is the mean and standard deviation of the sampling distribution of the sample proportions?

a)mean = 68.04, standard deviation = 0.0017

b)mean = 0.84, standard deviation = 0.0407

c)mean = 0.84, standard deviation = 0.0017

d)mean = 68.04, standard deviation = 0.0407

e)mean = 0.84, standard deviation = 0.9907

f)None of the above

Question 4 In a large population, 67% of the households have cable tv. A simple random sample of 256 households is to be contacted and the sample proportion computed. What is the probability that the sampling distribution of sample porportions is less than 73%?

a)0.4897

b)0.8796

c)0.9794

d)0.0206

e)0.1204

f)None of the above

Question 5 Which of the following statements isnottrue?

a)The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken.

b)The standard deviation of the sampling distribution of sample mean = ?/?n

c)The sampling distribution of sample mean is approximately normal, mound-shaped, and symmetric for n > 30 or n = 30.

d)The mean of the sampling distribution of sample mean is always the same as that of X, the distribution from which the sample is taken.

e)The larger the sample size, the better will be the normal approximation to the sampling distribution of sample mean.

f)None of the above

Question 6 Suppose a random sample of 50 measurements is selected from a population with a mean of 55 and a variance of 400. Select the pair that is the mean and standard error of x.

a)[50, 2.928]

b)[55, 2.828]

c)[55, 3.128]

d)[55, 2.928]

e)[55, 3.028]

f)None of the above

Question 7 A random sample of 1225 16-ounce cans of fruit nectar is drawn from among all cans produced in a run. Prior experience has shown that the distribution of the contents has a mean of 16 ounces and a standard deviation of .16 ounce. What is the probability that the mean contents of the 1225 sample cans is less than 15.992 ounces?

a)0.080

b)0.070

c)0.060

d)0.090

e)0.040

f)None of the above

Question 8 The World Health Organization’s (W.H.O.) recommended daily minimum of calories is 2600 per individual. The average number of calories ingested per capita per day for the US is approximately 2460 with a standard deviation of 500. If we take a random sample of 36 individuals from the US, what is the probability that the sample mean exceeds the W.H.O. minimum?

a)0.066

b)0.046

c)0.086

d)0.036

e)0.026

f)None of the above

Question 9 Suppose that a random sample of size 49 is to be selected from a population with mean 48 and standard deviation 7. What is the approximate probability thatXwill be within .5 of the population mean?

a)0.0569

b)0.6171

c)0.7658

d)0.3829

e)0.5829

f)None of the above

Question 10 Suppose that a random sample of size 36 is to be selected from a population with mean 49 and standard deviation 9. What is the approximate probability thatXwill be more than .5 away from the population mean?

a)0.0443

b)0.2611

c)0.4611

d)0.5222

e)0.7389

f)None of the above

Question 11 Lloyd’s Cereal company packages cereal in 1 pound boxes (16 ounces). A sample of 49 boxes is selected at random from the production line every hour, and if the average weight is less than 15 ounces, the machine is adjusted to increase the amount of cereal dispensed. If the mean for 1 hour is 1 pound and the standard deviation is 0.2 pound, what is the probability that the amount dispensed per box will have to be increased?

a)0.3773

b)0.2144

c)0.0144

d)0.9856

e)0.0287

f)None of the above

Question 12 The gas mileage for a certain model of car is known to have a standard deviation of 4 mi/gallon. A simple random sample of 64 cars of this model is chosen and found to have a mean gas mileage of 24.2 mi/gallon. Give the interval that would include the middle 95% for the sampling distribution of the mean gas mileage for this car model.

a)(22.22, 24.18)

b)(24.22, 26.18)

c)(15.36, 31.04)

d)(16.36, 32.04)

e)(23.22, 25.18)

f)None of the above

Question 13 The weight of a randomly selected bag of corn chips coming off an assembly line is a random variable with mean?=12oz. and standard deviation?=0.4oz. Suppose we pick five bags at random assume that weight of each of the bags are independent. The combined weight of these five bags is a random variable with a mean of

a)60 oz.

b)2.400 oz.

c)4.8 oz.

d)5 oz.

e)12 oz.

f)None of the above

Question 14 The weight of a randomly selected bag of corn chips coming off an assembly line is a random variable with mean?=9oz. and standard deviation?=0.4oz. Suppose we pick seven bags at random assume that weight of each of the bags are independent. The combined weight of these seven bags is a random variable with a standard deviation (in oz.) of

a)1.06 oz.

b)4.23 oz.

c)7 oz.

d)1.29 oz.

e)2.80 oz.

f)None of the above

Question 15 The weight of a randomly selected bag of corn chips coming off an assembly line is a random variable with mean?=11oz. and standard deviation?=0.2oz. The weight of a randomly selected bag of corn chips in pounds (1 pound = 16 oz.) is a random variable with standard deviation

a)2 pounds

b)0.01 pounds

c)3.20 pounds

d)2.20 pounds

e)0.05 pounds

f)None of the above

Question 16 The weight of a randomly selected bag of corn chips coming off an assembly line is a random variable with mean?=11oz. and standard deviation?=0.2oz. 4.Suppose we pick two bags at random from the assembly line. The difference in the weights of the two bags selected (the weight of the first bag minus the weight of the second bag) is a random variable with a mean (in oz.) of

a)22 oz.

b)0 oz.

c)11 oz.

d)0.20 oz.

e)0.10 oz.

f)None of the above