Applications with Standard Normal Distribution Assignment and Quiz 80%

The life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation 16 hours. What is the probability that a battery you buy lasts at most 100 hours?Standardize the variable.x = 100 is equivalent to z =

-1.75

For a standard normal distribution, find the approximate value of . Use the portion of the standard normal table below to help answer the question. 16% 34% 66% 84%

66%

Use the standard normal table to find P(z ≥ 1.4). Round to the nearest percent.

8%

Using the standard normal table, the probability that Seth's light bulb will last no more than 14,500 (P(z ≤ 1.25)) hours is about

89%

About what percentage of the data lies within 2 standard deviations of the mean in a normal distribution? 47.5% 68% 95% 99.7%

95%

How can you rewrite (z ≤ −1.75) in order to find the answer?

d

The probability that a battery you buy lasts at most 100 hours is about

4%

Using the standard normal table, about what percent of American adults have borderline-high cholesterol levels?

40%

Use the answer from the previous task to determine P(z < −2.1). 0.0179 0.5832 0.9821 1

0.0179

What is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question. 0.02 0.14 0.34 0.84

0.14

For a standard normal distribution, if , what is the value of ? 0.2116 0.2884 0.7116 0.7884

0.2884

The life of a manufacturer's compact fluorescent light bulbs is normal, with mean 12,000 hours and standard deviation 2,000 hours. Seth wants to find the probability that a light bulb he purchased from this manufacturer will last no more than 14,500 hours. How many standard deviations above the mean is 14,500 hours? 1.25 1.5 2.5

1.25

The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? Use the portion of the standard normal table below to help answer the question. 16% 32% 34% 84%

16%

What is P(0.6 ≤ z ≤ 2.12)?

26%

What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question. 0.02 0.16 0.18 0.82

NOT: 0.82

Which of the following statements is equivalent to ?

NOT: d

If a data value in a normal distribution has a negative z-score, which of the following must be true? The data value must be negative. The data value must be positive. The data value must be less than the mean. The data value must be greater than the mean.

The data value must be less than the mean.

The probability that a random variable is greater than or equal to z standard deviations from the mean in a standard normal distribution is p%. What can be said with certainty about the probability that the random variable is less than or equal to -z standard deviations from the mean? The probability is less than p%. The probability is equal to p%. The probability is greater than p%. The probability is not equal to p%.

The probability is equal to p%.

Explain how to use the standard normal table to find the probability associated with the shaded area under the curve.

The standard normal table gives areas under the curve to the left of z-scores. Find the probability in the standard normal table that a value is to the left of 1.9. Find the probability in the standard normal table that a value is to the left of 0.4. Subtract the probability of a value being to the left of 0.4 from the probability of a value being to the left of 1.9.

For a standard normal distribution, which of the following variables always equals 0?

a

Which is equivalent to P(z ≥ 1.4)?

b

Which of the following statements is equivalent to P(z < −2.1)? P(z > -2.1) 1-P(z < 2.1) P(z < 2.1) 1-P(z > 2.1)

b

Which statement represents the percent of American adults with total cholesterol scores in the borderline-high range? Cholesterol levels in the blood are an important health measure. High cholesterol is a risk factor of serious conditions, such as heart disease. This table shows the general guidelines for total cholesterol scores. Total cholesterol scores for American adults are normally distributed, with μ = 200 mg/dL. Use σ= 30 mg/dL.

c