Business Stats Test 7b

A binomial distribution has 50 trials (n = 50) with a probability of success of 0.50 (π = 0.50). To use the normal distribution to approximate the binomial, what are the mean and standard deviation?

µ = 25 and σ = 3.5355

A binomial distribution has 100 trials (n = 100) with a probability of success of 0.25 (π = 0.25). To apply the normal distribution to approximate the binomial, what are the mean and standard deviation?

µ = 25 and σ = 4.33

The standard deviation of any uniform probability distribution is ____________.

√(b-a)^2 / 12

A binomial distribution has 100 trials (n = 100) with a probability of success of 0.25 (π = 0.25). We would like to find the probability of 34 or more successes using the normal distribution to approximate the binomial. z-score should be used?

1.963

The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant is 15.0 pounds, and the standard deviation of the normally distributed weights is 1.75 pounds. Of the 200 plants 13 and 16 pounds?

118

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's mean?

135 minutes

A study of a company's practice regarding the payment of invoices revealed that an invoice was paid an average of 20 days after it was received. Assuming that the distribution is normal, what percent of the invoices were paid within 15 days of receipt?

15.87%

The annual commissions per salesperson employed by a retailer of mobile communication devices averaged $40,000, with a standard deviation of $5,000. What percent of the salespersons earn between $32,000 and $42,000?

60.06%

A college professor noted that the grades of his students in an introductory statistics class were normally distributed with a mean of 76.5 and a standard deviation of 9. If 67.36% min score of those students receiving a grade of at least a C?

72.45

A binomial distribution has 100 trials (n = 100) with a probability of success of 0.25 (π = 0.25). We would like to find the probability of 75 or more successes using the normal distribution to approximate the binomial. calculate a z-score?

74.5

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, what test score separates the top 25% of the students from the lower 75% of students?

74.69

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's standard deviation?

8.66 minutes

A normally distributed random variable has _________.

Any value between -∞ and + ∞

The shape of any uniform probability distribution is ____________.

Rectangular

The weekly incomes of a large group of executives are normally distributed with a mean of $2,000 and a standard deviation of $100. What is the z-score for an income of $2,100?

1.00

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is less than 135 minutes?

0.50

Consider a standard normal random variable z. What is the value of z if the area to the right of z is 0.2643?

0.63

If an average of 12 customers is served per hour, what is the probability that the next customer will arrive in 6 minutes or less?

0.70

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, what is the probability that a student scored greater than 65?

0.7611

If an average of 60 customers are served per hour, then one customer arrives every ________.

1 minute

The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68% of the incomes lie between what two incomes?

$36,400 and $38,000

The mean of any uniform probability distribution is _________.

(a + b)/2

The average score of 100 students taking a statistics final was 70, with a standard deviation of 7. Assuming a normal distribution, what is the probability that a student scored 90 or higher?

0.0021

The weight of cans of fruit is normally distributed with a mean of 1,000 grams and a standard deviation of 50 grams. What percent of the cans weigh 860 grams or less?

0.0026

For a standard normal distribution, what is the probability that z is greater than 1.75?

0.0401

A cola-dispensing machine is set to dispense a mean of 2.02 liters into a container labeled 2 liters. distributed with a standard deviation of 0.015 liters. What is the probability a container will have less than 2 liters?

0.0918

The mean amount spent by a family of four on food is $500 per month with a standard deviation of $75. Assuming that the food costs are normally distributed, what is the probability that a family spends less than $410 per month?

0.1151

The average starting salary of individuals with a master's degree in statistics is normally distributed with a mean of $48,000 and a standard deviation of $6,000. of at least $55,500?

0.121

What is the area under the normal curve between z = -1.0 and z = -2.0?

0.1359

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is more than 140 minutes?

0.333

Customers of the Key Refining Company charge an average of $70 per month. with a standard deviation of $10. What is the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83?

0.4032

The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. What is the probability of a weight between 415 pounds and the mean of 400 pounds?

0.4332

The employees of Cartwright Manufacturing are awarded efficiency ratings. The distribution of the ratings approximates a normal distribution. The mean is 400, the standard deviation is 50. What is the area under the normal curve between 400 and 482?

0.4495

If an average of 12 customers is served per hour, what is the probability that the next customer will arrive in 3 minutes or less?

0.45

What is the area under the normal curve between z = 0.0 and z = 1.79?

0.4633

What is the probability that z is between 0.0 and 2.0?

0.4772

Consider a continuous random variable x, which is uniformly distributed between 65 and 85. The probability of x taking on a value between 75 to 90 is ________.

0.50

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is between 125 and 140 minutes?

0.50

The total area of a normal probability distribution is _______.

1.00

An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use before they failed is 19.0 hours. 1.2 hours. About 95.44% of the batteries failed between what two values?

16.6 and 21.4

A binomial distribution has 50 trials (n = 50) with a probability of success of 0.50 (π = 0.50). We would like to find the probability of 34 or more successes using the normal distribution to approximate the binomial. what z score?

2.404

Ball-Bearings, Inc. produces ball bearings automatically on a Kronar BBX machine.the mean diameter is set at 20.00 mm. to be 0.150 mm. What percent of the ball bearings will have diameters of 20.27 mm or more?

3.59%

A national manufacturer of unattached garages discovered that the distribution of the time for two construction workers to erect the Red Barn mod32 hours and a standard deviation of 2 hours. What percent of 32 and 34 hours to erect?

34.13%

Management is considering a bonus system to increase production. One suggest the highest 5% average of 4,000 units of a small assembly is produced during a week. 60 units. on the upper 5% of production, the bonus will be paid on how many units or more?

4099

Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. mean of 47,900 miles and a standard deviation of 2,050 miles.more than 5% of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce?

44,518

The mean of a normal probability distribution is 500 and the standard deviation is 10. About 95% of the observations lie between what two values?

480 and 520

If an average of 12 customers are served per hour, then one customer arrives every ________.

5 minutes

A large manufacturing firm tests job applicants. Test scores are normally distributed with a mean of 500 and a standard deviation of 50. What is the lowest score a new hire must earn to qualify for a responsible position?

578

The average score of 100 students taking a statistics final was 70, with a standard deviation of 7. Assuming a normal distribution, what test score separates the top 5% of the students from the lower 95% of the students?

81.55

An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8. 10% To the nearest percent, what is the dividing point between an A and a B grade?

85

For the normal distribution, the mean plus and minus two standard deviations will include about what percent of the observations?

95%

For a normal distribution, what is the likelihood (expressed as a percentage) that a random variable is within plus and minus two standard deviations of the mean?

95.44%

A new extended-life light bulb has an average life of 750 hours, with a standard deviation of 50 hours. If the life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 900 hours?

99.47%

Tables of normal distribution probabilities are found in many statistics books. These probabilities are calculated from a normal distribution with ___________.

A mean of 0 and a standard deviation of 1

Which of the following is a characteristic of the normal probability distribution?

It's bell-shaped

Two normal distributions are compared. One has a mean of 10 and a standard deviation of 10. The second normal distribution has a mean of 10 and a standard deviation of 2. Which of the following is true?

The dispersions of the distributions are different

The upper and lower limits of a uniform probability distribution are __________.

The maximum and minimum values of the random variable

What is an important similarity between the uniform and normal probability distributions?

The mean and median are equal.

Which of the following is true in a normal distribution?

The mean divides the distribution into two equal areas.

Which of the following is true regarding the normal distribution?

The mean, median, and mode are all equal

The standard normal probability distribution is unique because it has _________.

a mean of 0 and standard deviation of 1

In an illustration of a normal probability distribution, a shaded area represents _______.

a probability

The mean score of a college entrance test is 500; the standard deviation is 75. The scores are normally distributed. What percent of the students scored below 320?

about 0.82%

The weekly mean income of a group of executives is $1,000 and the standard deviation of this group is $100. The distribution is normal. What percent of the executives have an income of $925 or less?

about 23%

The z-value for a standard normal distribution ________.

can be either positive or negative

What is a normal distribution with a mean of 0 and a standard deviation of 1 called?

standard normal distribution

The center of a normal probability distribution is ________.

the mean of the distribution