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Problems I am stuck on...

Problems I am stuck on my homework with:

1.With regards XXXXX XXXXX standard normal distribution complete the following:

(a) Find P(z > 0), the percentage of the standard normal distribution above the z-score of 0.

(b) Find P(z < 1), the percentage of the standard normal distribution below the z-score of 1.

(c) Find P(-1.23 < z -3).

(e) Find the z-score that separates the lower 25% of standarized scores from the top 75% . . . that is find the z-score corresponding to P25.

2.For a certain population of students, weight is normally distributed with a mean of 120 pounds and a standard deviation of 25 pounds. Determine the following:

(a) Determine the z-score for a student that weighs 95 pounds. Then find the z-score for one that weighs 170 pounds.

(b) If x represents a possible raw-score weight, find P(x > 135).

(c) Find P(90 < x < 140) and give an interpretation of this value.

(d) The top 5% of all students in this group are to be considered overweight. Determine the raw-score weight which separates the overweight students from the rest of the group.

3.Answer the following based upon the implications of the Central Limit Theorem.

(a) How does the mean of the sampling distribution of all possible sample means from a population compare to the mean of the population?

(b) How does the standard deviation of the sampling distribution of all possible sample means from a population compare to the standard deviation of the population?

4.Let us assume that the price of regular unleaded gasoline across the nation is normally distributed with a mean of $3.10 and a standard deviation of $0.28.

(a) Accurately describe the shape and scaling(mean/st.dev.) of the graph of the distribution for the population of all prices across the nation for regular unleaded gasoline.

(b) If all possible samples of size fifty from the population of these gasonline prices are drawn and the mean is found for each sample, describe the shape and scaling (mean/st.dev.) on the graph of the sampling distribution for these sample mean values as theorized by the Central Limit Theorem.

(c) Find the probability that the price from a single randomly selected gas station will be more than $3.40. Based upon your results, would it be unusual to find an individual gas station where the price is more than $3.40?

(d) Find the probability that the mean from 50 randomly selected gas stations will be more than $3.40. Based upon your results, would it be unusual to find a sample of 50 randomly selected gas stations where the average price is more than $3.40?

5.A 90 % confidence interval for a situation is developed and is given by the following 48 < µ < 64.

(a) Give the value of the sample mean that was used in developing this interval.

(b) Give the value of the margin of error that was used in developing this interval .

6.Calculate the appropriate critical z-value for each of the following confidence levels?

(a) 95% confidence level:

(b) 80% confidence level:

7.What happens to the size (width) of a confidence interval in a problem if:

(a) the percent of desired confidence (confidence level) increases from 80% to 90%? Does it get wider or narrower?

(b) the size of the sample used to produce the confidence interval is decreased?

(c) the margin of error is decreased?

8.A survey of 400 people who took vacations revealed that 242 of them flew to their destination. Give a 95% confidence interval for the percentage of all people who fly when they take a trip. Does it appear statistically correct to conclude that more than 50% of all people who take vacations will fly to their destination? Why or why not?

9.Suppose you want to estimate the percentage of adults who fly to their vacation destination and you want your estimate to be within 3 percentage points of the correct population measure, based upon a 95% confidence level. What size sample is required?--(assume that no estimate of "p-hat" is known.)

10.The average systolic blood pressure readings from a random sample of 100 people is 123.4 (assume a population standard deviation of 15.6). Based upon a desired 99% confidence level, determine the margin of error E in this sample statistic and then give the associated confidence interval.

11.You need to estimate the mean useful life of a certain brand of light bulb to within 20 hours with 98% confidence. Previous studies indicate that the standard deviation for the light bulb is 40 hours. How many observations should your sample contain to meet this desired level of accuracy?

1.With regards XXXXX XXXXX standard normal distribution complete the following:

(a) Find P(z > 0), the percentage of the standard normal distribution above the z-score of 0.

(b) Find P(z < 1), the percentage of the standard normal distribution below the z-score of 1.

(c) Find P(-1.23 < z -3).

(e) Find the z-score that separates the lower 25% of standarized scores from the top 75% . . . that is find the z-score corresponding to P25.

2.For a certain population of students, weight is normally distributed with a mean of 120 pounds and a standard deviation of 25 pounds. Determine the following:

(a) Determine the z-score for a student that weighs 95 pounds. Then find the z-score for one that weighs 170 pounds.

(b) If x represents a possible raw-score weight, find P(x > 135).

(c) Find P(90 < x < 140) and give an interpretation of this value.

(d) The top 5% of all students in this group are to be considered overweight. Determine the raw-score weight which separates the overweight students from the rest of the group.

3.Answer the following based upon the implications of the Central Limit Theorem.

(a) How does the mean of the sampling distribution of all possible sample means from a population compare to the mean of the population?

(b) How does the standard deviation of the sampling distribution of all possible sample means from a population compare to the standard deviation of the population?

4.Let us assume that the price of regular unleaded gasoline across the nation is normally distributed with a mean of $3.10 and a standard deviation of $0.28.

(a) Accurately describe the shape and scaling(mean/st.dev.) of the graph of the distribution for the population of all prices across the nation for regular unleaded gasoline.

(b) If all possible samples of size fifty from the population of these gasonline prices are drawn and the mean is found for each sample, describe the shape and scaling (mean/st.dev.) on the graph of the sampling distribution for these sample mean values as theorized by the Central Limit Theorem.

(c) Find the probability that the price from a single randomly selected gas station will be more than $3.40. Based upon your results, would it be unusual to find an individual gas station where the price is more than $3.40?

(d) Find the probability that the mean from 50 randomly selected gas stations will be more than $3.40. Based upon your results, would it be unusual to find a sample of 50 randomly selected gas stations where the average price is more than $3.40?

5.A 90 % confidence interval for a situation is developed and is given by the following 48 < µ < 64.

(a) Give the value of the sample mean that was used in developing this interval.

(b) Give the value of the margin of error that was used in developing this interval .

6.Calculate the appropriate critical z-value for each of the following confidence levels?

(a) 95% confidence level:

(b) 80% confidence level:

7.What happens to the size (width) of a confidence interval in a problem if:

(a) the percent of desired confidence (confidence level) increases from 80% to 90%? Does it get wider or narrower?

(b) the size of the sample used to produce the confidence interval is decreased?

(c) the margin of error is decreased?

8.A survey of 400 people who took vacations revealed that 242 of them flew to their destination. Give a 95% confidence interval for the percentage of all people who fly when they take a trip. Does it appear statistically correct to conclude that more than 50% of all people who take vacations will fly to their destination? Why or why not?

9.Suppose you want to estimate the percentage of adults who fly to their vacation destination and you want your estimate to be within 3 percentage points of the correct population measure, based upon a 95% confidence level. What size sample is required?--(assume that no estimate of "p-hat" is known.)

10.The average systolic blood pressure readings from a random sample of 100 people is 123.4 (assume a population standard deviation of 15.6). Based upon a desired 99% confidence level, determine the margin of error E in this sample statistic and then give the associated confidence interval.

11.You need to estimate the mean useful life of a certain brand of light bulb to within 20 hours with 98% confidence. Previous studies indicate that the standard deviation for the light bulb is 40 hours. How many observations should your sample contain to meet this desired level of accuracy?

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