Chapter 6-6

Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 116 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eliible voters aged 18-24, 22% of them voted. Probability that exactly 28 voted The probability that exactly 28 of 116 eligible voters voed is _____.

The probability that exactly 28 of 116 eligible voters voed is _0.0777_. vassarstats.net/binomialX.html approximation via normal

Use a normal approximation to find the probability of the indicated number of voters. In this case, assumterm-5e that 192 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that fewer than 48 voted. The probability that fewer than 48 of 192 eligible voters voted is _____.

The probability that fewer than 48 of 192 eligible voters voted is _0.8210_. binomcdf(192,0.22,47.5) = 0.8210

Assume that 35.8% of people have sleepwalked. Assume that in a random sample of 1541 adults, 573 have sleepwalked. a) Assuming that the rate of 35.8% is correct, the probability that 573 or more of the 1541 adults ahve sleepwalked is _____. b) Is that result of 573 or more significantly high? _____ because the probability of this event is __________ than the probability cutoff that corresponds to a singificant event, which is _____. c) What does the result suggest about the rate of 35.8%? A) Since the result of 573 adults that have sleepwalked is not significantly high, it is not strong evidence supporting the assumed rate of 35.8%. B) Since the result of 573 adults that have sleepwalked is significantly high, it is strong evidence against the assumed rate of 35.8% C) Since the result of 573 adults that have sleepwalked is not significantly high, it is not strong evidence agains the assumed rate of 35.8%. D) Since the result of 573 adults that have sleepwalked is not significantly high, it is strong evidence against the assumed rate of 35.8%. E) Since the result of 573 adults that have sleepwalked is significantly high, it is not strong evidence against the assumed rate of 35.8%. F) The results do not indicate anything about the scientist's assumption.

a) Assuming that the rate of 35.8% is correct, the probability that 573 or more of the 1541 adults ahve sleepwalked is _0.1344_. Use Binomial Calculator Cumulative probability: P(X > x) b) Is that result of 573 or more significantly high? _No,_ because the probability of this event is _greater_ than the probability cutoff that corresponds to a singificant event, which is _0.05_. c) What does the result suggest about the rate of 35.8%? C) Since the result of 573 adults that have sleepwalked is not significantly high, it is not strong evidence agains the assumed rate of 35.8%.

Based on a smartphone survey, assume that 51% of adults with smartphones use them in theaters. In a separate survey of 257 adults with smartphones, it is found that 114 use them in theaters. a) If the 51% rate is correct, the probability of getting 114 or fewer smartphone owners who use them in theaters is _____. b) Is the result of 114 significantly low? __________ beacuse the probability of this event is __________ than the probaility cutoff that corresponds to a significant event, which is _________.

a) If the 51% rate is correct, the probability of getting 114 or fewer smartphone owners who use them in theaters is _0.0193_. binomcdf(257,0.51,114) = 0.0193 b) Is the result of 114 significantly low? _Yes_ beacuse the probability of this event is _less_ than the probaility cutoff that corresponds to a significant event, which is _0.05_.

If np ≥ 5 and nq ≥ 5, estimate P (at least 8) with n = 13 and p = 0.5 by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq < 5, then state that the normal approximation is not suitable. a) P(at least 8) = _____ b) The normal distribution cannot be used.

a) P(at least 8) = _0.291_ 1-binomcdf(13,0.5,7)=0.291

If np ≥ 5 and nq ≥ 5, estimate P (fewer than 2_ with n = 13 and p = 0.4 by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq < 5, then state that the normal approxmiation is not suitable. a) P(fewer than 2) = _____ b) The normal approximation is not suitable.

a) P(fewer than 2) = _0.0183_ n=13 p=0.4 u=np=(13)(0.4)=5.2 1-0.4=0.6 o=13(0.4)(0.6)=3.12=sq. rt. of 3.12= 1.77 normalcdf(-10000,1.5,5.2,1.77)=0.0183

In a study of 319,243 cell phone users, it was found that 118 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is a 0.000446 probability of a person developing cancer of the brain or nervious system. We thereofore expect about 143 cases of such cancer in a group of 319,243 people. Estimate the probability of 118 or fewer cases of such cancer in a group of 319,243 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous system? a) P(x ≤ 118)= _____ b) What does the result from part (a) suggest about the media reports? A) The media reports appear to be incorrect because one would expect that more than 95 cell phone users would develop cancer. In​ fact, the study may offer significant evidence to suggest that cell phone use decreases the probability of developing cancer. B) The media reports appear to be correct because one would expect that less than 95 cell phone users would develop cancer and the study offers significant evidence to support this. C) The media reports appear to be correct because one would expect that more than 72 cell phone users would develop cancer and the study offeres significant evidence to support this.

a) P(x ≤ 118)= _0.0203_ binomcdf(319243,0.000446,118)= 0.0203 b) What does the result from part (a) suggest about the media reports? A) The media reports appear to be incorrect because one would expect that more than 95 cell phone users would develop cancer. In​ fact, the study may offer significant evidence to suggest that cell phone use decreases the probability of developing cancer.

The value given below is discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. Probability of more than 6 passengers who do not show up for a flight. a) The area to the right of 6.5 b) The area to the left of 5.5 c) The area to the right of 5.5 d) The area between 5.5 and 6.5 e) The area to the left of 6.5

a) The area to the right of 6.5

If np ≥ 5 and nq ≥ 5, estimate P(more than 5) with n = 14 and p = 0.3 by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq < 5, then state that the normal approximation is not suitable. a) P(more than 5) = _____ b) The normal distribution cannot be used.

b) The normal distribution cannot be used. u=14(0.3)=4.2 is not more than 5

Which statement below indicates the area to the left of 19.5 before a continuity correction is used? a) At least 19 b) Less than 19 c) At least 20 d) At most 19

d) At most 19

Why must a continuity correction be used when using the normal approximation for the binomial distribution? a) The sample size is less than 5% of the size of the population. b) The normal distribution is a discrete probability distribution being used as an approximation to the binomial distribution which is a continuous probability distribution. c) The probability of an event is particularly small. d) The normal distribution is a continuous probability distribution being used an an approximation to the binomal distribution which is a discrete probability distribution.

d) The normal distribution is a continuous probability distribution being used an an approximation to the binomal distribution which is a discrete probability distribution.