Question

In: Statistics and Probability

In which situation may the sample proportion safely be assumed to follow a normal distribution? Select...

In which situation may the sample proportion safely be assumed to follow a normal distribution?

Select one:

a. 8 successes in a sample of 72 items.

b. 5 successes in a sample of 20 items.

c. 9 successes in a sample of 200 items.

d. 12 successes in a sample of 500 items.

Solutions

Expert Solution

a. Here p=8/72=0.1111 and n=72 so np=8<10

So it is not normal

b. Here p=5/20=0.25 and n=20, so np=20*0.25=5<10

So it is not normal

c. Here p=9/200=0.045 and n=200, so np=200*0.045=9

So it is not normal

d. Here p=12/500=0.0240 and n=500, so np=500*0.0240=12>10

Hence it is normal

orchestra answered 2 years ago
Next > < Previous

Related Solutions

The amount of a loss, Y, is assumed to follow a Normal distribution with a mean...
The amount of a loss, Y, is assumed to follow a Normal distribution with a mean of ? and a variance of ?^2. The median of Y is 56.5 and the 59.1-th percentile of Y is 56.776. Determine P(Y > 60 ).
The score on a proficiency measure is assumed to follow a normal distribution. A switch to...
The score on a proficiency measure is assumed to follow a normal distribution. A switch to better lighting might change the score. A random sample of 30 people taken during the year before the switch to better light yielded a mean score of 600 and a variance of 400. A different random sample of 30 people after the switch had a mean of 610 and a variance of 441. Important: use a degrees of freedom nu=80 for the t statistic....
The IQ scores of children in a city are assumed to follow a normal distribution with...
The IQ scores of children in a city are assumed to follow a normal distribution with unknown mean μ and known variance σ^2. A random sample IQ scores with a size of 25 is drawn by a researcher. Based on this sample, a 97% confidence interval for μ is found to be (91.49,104.51). (a) Show that σ=15. (b) Another random sample of IQ scores with a size of 11 drawn and the scores are recorded as follows: 134, 95,102, 99,...
Proportion data follow the binomial distribution, which can be approximated by the normal distribution if np>=5...
Proportion data follow the binomial distribution, which can be approximated by the normal distribution if np>=5 and nq>=5 True or False? The sample Proportion p̄=x/n where x is the number of successes and n is the sample size True or false? The Type-II error β is the probability of failing to reject a true null Hypothesis Ho. True or false? The only way to lower the probability of both errors α and β at the same time, is to decrease...
Suppose the current measurements in a strip of wire are assumed to follow a normal distribution...
Suppose the current measurements in a strip of wire are assumed to follow a normal distribution with a mean of 10 mA and a variance of 4 (mA)^2. a. What is the probability that a measurement will exceed 13 mA? b. What is the probability that a current measurement is between 9 and 11 mA? c. Determine the value for which the probability that a current measurement is below this value is 0.98. Please show all steps and explanations. Thank...
1. Glucose levels in patients free of diabetes are assumed to follow a normal distribution with...
1. Glucose levels in patients free of diabetes are assumed to follow a normal distribution with a mean of 120 and a standard deviation of 16. What is the probability that the mean glucose level is LESS THAN 115 in a sample of 12 patients? Group of answer choices a.1.08 b.0.8599 c.0.1401 d.-1.08 2. I cant seem to find the right answer here Glucose levels in patients free of diabetes are assumed to follow a normal distribution with a mean...
The cholesterol level in children aged 10-15 is assumed to follow a normal distribution with a...
The cholesterol level in children aged 10-15 is assumed to follow a normal distribution with a mean of 175 and a standard deviation of 20. What is the probability of selecting a child at 10-15 years with cholesterol level higher than 190? What is the probability of selecting a child at 10-15 years with cholesterol level between 165 and 190? What is the interval of cholesterol level of a child 10-15 years higher than 75% and lower than top 10%...
the height in children aged 10-15 is assumed to follow a normal distribution with a mean...
the height in children aged 10-15 is assumed to follow a normal distribution with a mean of 165 with a standard deviation of 15. c)what proportion of children 10-15 years of age have height less than 145? d)what proportion of children 10-15 years of age have height between 125 and 210? e)how tall does a child 10-15 years of age have to be shorter than 95% of children? f)how tall does a child 10-15 years of age have to be...
For the shape of the distribution of the sample proportion to be approximately? normal, it is required that
Fill in the blanks to complete the following statements.Bold left parenthesis a right parenthesis(a)For the shape of the distribution of the sample proportion to be approximately? normal, it is required that?np(1minus??p)greater than or equals??______.Bold left parenthesis b right parenthesis(b)Suppose the proportion of a population that has a certain characteristic is0.9The mean of the sampling distribution ofModifyingAbove p with caretpfrom this population ismu Subscript ModifyingAbove p with caret?pequals=?______.?(This is a reading assessment question. Be certain of your answer because you only...
The life of a 9-volt battery is said to follow a Normal distribution. A sample of...
The life of a 9-volt battery is said to follow a Normal distribution. A sample of 75 batteries is tested and a mean life of the sample is found to be 50.25 hours with a standard deviation of 1.5 hours. Use α = 0.05. (a) Is it believable that mean battery life exceeds 50 hours? (b) Find the P-value for the test conducted in part a.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT