What is the area under the normal curve

Assignment Help Basic Statistics

Reference no: EM132403085

Questions -

Q1. Assume that the probability of the binomial random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed.

Find the probability that less than 58 households have a gas stove.

What is the area under the normal curve that describes the probability that less than 58 households have a gas stove?

A. The area between 57.5 and 58.5

B. The area to the left of 58.5

C. The area to the left of 57.5

D. The area to the right of 57.5

E. The area to the right of 58.5

Q2. Assume that the probability of the binomial random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed.

Find the probability that there are exactly 5 defective parts in a shipment.

What is the area under the normal curve that describes the probability that there are exactly 5 defective parts in a shipment?

A. The area to the right of 4.5

B. The area to the right of 5.5

C. The area to the left of 4.5

D. The area to the left of 5.5

E. The area between 4.5 and 5.5

Q3. Whether a randomly selected individual has blood-type O-negative is a binomial random variable. Assume that its probability will be approximated using the normal distribution. Describe the area under the normal curve that will be computed in order to determine the probability that the number of people with blood type O-negative is between 12 and 29, inclusive.

Describe the area under the normal curve. Choose the correct answer below.

A. Left of x = 11.5

B. Between x = 11.5 and x = 29.5

C. Right of x = 29.5

D. Between x = 12 and x = 29

Q4. Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.

n = 62, p = 0.4, and X = 37

Q5. Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.

n = 40, p = 0.35, and X = 15

Q6. A certain flight arrives on time 89 percent of the time. Suppose 157 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that

(a) exactly 146 flights are on time.

(b) at least 146 flights are on time.

(d) between 136 and 142, inclusive are on time.

Q7. In studies for a medication, 11 percent of patients gained weight as a side effect. Suppose 490 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that

(a) exactly 54 patients will gain weight as a side effect.

(b) no more than 54 patients will gain weight as a side effect.

Q8. According to a study, 72% of all males between the ages of 18 and 24 live at home. (Unmarried college students living in a dorm are counted as living at home.) Suppose that a survey is administered and 183 of 240 respondents indicated that they live at home.

(a) Use the normal approximation to the binomial to approximate the probability that at least 183 respondents live at home.

(b) Do the results from part (a) contradict the study?

Reference no: EM132403085

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