**MIAMI DADE COLLEGE****:** STA 2023 – Statistical Methods

**Use the following distribution to answer questions 3 and 4.**

**1) What is the total area under the curve?**

A) 1 B) 3 C) 2500 D) 3000

**2)** **What is the mean?**

A) 1 B) 3 C) 2500 D) 3000

· **Find the area under the standard normal distribution curve.**

**3)** **Between z = 0 and z = .75**

A).07734 B) .7734 C) .2734 D) 27.34

**4)** **To the left of z = -1.39**

A) 8.23 B) .0082 C) .82 D) .0823

**5)** **To the left of z =** **1.23**

A) .8907 B) .1093 C) .2266 D) 89.07

**6)** **To the right of z =** **1.23**

A) .8907 B) .1093 C) .2266 D) 89.07

**7)** **Between z = – 0.75 and ** **z =** **1.23**

A) .8907 B) .1093 C) .2266 D) .6641

· **The average credit card debt for college seniors is $3262. If the debt is normally distributed with a standard deviation of $1100. Find these probabilities.**

8) **That the senior owes at least $1000**

A).9803 B) 9.803 C) -2.06 D) .0206

**9)** **That the senior owes more than $4000**

A) .7486 B) .1486 C) .2514 D) 51.40

**10)** **To qualify for a police academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to qualify. Assume the test scores are normally distributed.**

A) 226 B) 1.28 C) 90% D) 200

· **The average credit card debt for college seniors is $3173. If the debt is normally distributed with a standard deviation of $1120. Find these probabilities.**

**11) What is the probability that a randomly selected undergraduate has a credit balance less than $2700?**

A) -0.42 B) -2.11 C) .3372 D) .0174

**12) You randomly select undergraduate. What is the probability ****that their mean**** balance less than $2700?**

A) -0.42 B) -2.11 C) .3372 D) .0174

**13) In a binomial experiment. N= 45, p = .47, and q = 0.53. Find the mean?**

A) 21.15 B) 23.85 C) 3.35 D) 4.6

**14) In a binomial experiment. N= 45, p = .47, and q = 0.53. Find the standard deviation?**

A) 21.15 B) 23.85 C) 3.35 D) 4.6

**15)** **In a recent study of 35 ninth-grade students, the mean number of hours per week that they played video games was 16.6. The standard deviation of the population was 2.8. Find the 95 % confidence interval of the mean of the time playing video games. **

A) (157, 175) B) (15.7, 17.5) C) (-15.7, -17.5) D) (1.57, 1.75)

**16) A scientist wishes to estimate the average depth of a river. He wants to be 99% confident that the estimate is accurate within 2 feet. From a previous study, the standard deviation of the depths measured was 4.33 feet. Find the Minimum Sample Size Needed for an Interval Estimate of the POPULATION MEAN**

A) 21.2 B) 32 C) .32 D) 25

**17) ** **Ten randomly selected people were asked how long thy sept at night. The mean time was 7.1 hours, and the standard deviation was 0.78 hours. Find the 95% confidence interval of the meantime. Assume the variable is normally distributed**

A) (157, 175) B) (15.7, 17.5) C) (65.4, 76.6) D) (6.54, 7.66)

**18)** **A survey of 1500 adults found that 39% said that they would take more vacations this year than last year. Find the 95% confidence interval for the true proportion of adults who said that they will travel more this year.**

A) – .365<P<-.415 B) .365<P<.415 C) 3.65<P<4.15 D) 36.5<P<41.5

**19)** **A researcher wishes to estimate with 95% confidence, the proportion of the people who own a home computer. A previous study shows that 40% of the interviewed had a computer at home. The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size necessary?**

A) 1.96 B) 2305 C) 1305 D) 23.04

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