### Test 02 | 7.1 to 9.4 • Name:

##### Chapter Seven: Normal curve problems
NameDuration/minutes
Daniel S.43
Elvis57
Lee Ling73
Israel79
Aloka79
Paul86
Joshua94
Branson98
Tosiwo98
LJ101
Jake105
Penina105
Charles111
Emmanuel111
Edwin113
Ermine115
Dalina117
Daniel M.118

Use the data in the table shown to calculate the following values.

1. x = ______________ Calculate the sample mean.
2. sx = ______________ Calculate the sample standard deviation.

Presume that the arrival times of the walkers and runners were normally distributed. The following problems derive from chapter seven. Use the standard normal distribution to determine your answers. Use the sample mean x from question one for µ, and the sample standard deviation sx from question two for σ in the questions below. Here the variable is x and NOT x.

1. ______________ What percentage of walkers and runners arrived in 94.61 minutes or less?
2. ______________ What percentage of walkers and runners arrived after 115.93 minutes or later?
3. ______________ The walk/run started at four. Dark hit the road just after six, about 130 minutes after the start. What percentage of walkers/runners would be expected to have finished during the first 130 minutes?
4. ______________ By what duration in minutes x had 10% of the walkers/runners arrived?
##### Chapter nine: Confidence interval calculations

Use the sample mean x from question one and the sample standard deviation sx from question two and the data given in the first table to calculate a 95% confidence interval for the population mean µ duration in minutes using the student's t-distribution.

1. sample size: n = ______________
2. confidence level: c = ______________
3. degrees of freedom: = ______________
4. t-critical: tc = ______________
5. Error tolerance E: = ______________
6. Calculate the confidence interval for the population mean arrival time:

P( ___________ ≤ µ ≤ ___________ ) = 0.95
7. _________ In quiz eight we found a mean duration of 103 minutes (1.7 hours). Does our confidence interval include 103 minutes?

For fun if you finish early: Lee Ling jogged and juggled the 10.329 kilometers from the college to spanish wall. Measurements done at the PICS track found that during a 2.73 minute lap, Lee Ling makes 69.5 cycles of the balls where one cycle is the return of the number one ball to the right hand. With three balls, the number of tosses per hand per 2.73 minutes is thrice 69.5 or 208.5 tosses per hand each and every 2.73 minutes. Use these numbers and his time of 73 minutes to estimate the number of tosses per hand from the college to spanish wall. _______________________

Statistic or Parameter Symbol Equations Excel
Chapter seven: Normal statistics
Calculate a z value from an x z = =STANDARDIZE(x, µ, σ)
Calculate an x value from a z x = z σ + µ =z*σ+µ
Find a probability p from a z value     =NORMSDIST(z)
Find a z value from a probability p     =NORMSINV(p)
Chapter eight: Distribution of the sample mean x
Calculate a z-statistic from an x z =(x - µ)/(sx/SQRT(n))
Calculate a t-statistic (t-stat) t =(x - µ)/(sx/SQRT(n))
Calculate an x from a z   =µ + zc*sx/sqrt(n)
Chapter nine: Confidence interval statistics
Find a tc value from a confidence level c and sample size n tc   =TINV(1-c,n-1)
Calculate an error tolerance E of a mean for any n ≥ 5 using sx. E =tc*sx/SQRT(n)
Calculate a confidence interval for a population mean µ from a sample mean x and an error tolerance E   x-E≤ µ ≤x+E