Statistics Problems: Probability, Confidence Intervals, and Sampling

College Male Students’ Heights

1. Suppose College male students’ heights are normally distributed with a mean of µ = 69.5 inches and a standard deviation of σ =2.8 inches

a. If one male student is randomly selected, find the probability that his height is less than 65.2 inches or greater than 71.2 inches. 

b. How tall is Mauricio if only 30.5% of students are taller than him (2 decimal places)?

c. How tall is Mike if 30.5% of students shorter than 75 inches are taller than Mike? (In other words, there are 30.5% of students between Mike’s height and 70 inches. How tall is Mike?) 

d. If 25 male students are randomly selected, find the probability that they have a mean height no higher than 70.2 inches.

2. The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic device. After observing a number of workers assembling similar devices, she estimates that the standard deviation is 0.25 hour. How large a sample of workers should she select if she wishes to estimate the mean assembly time to within 3.2 minutes at a 98% confidence level?

3. In a crash test of 26 minivans, collision repair costs are found to have a distribution that is roughly bell shaped, with a mean of $1850 and a standard deviation  of $340. Construct a 95% confidence interval for the mean repair cost in all such vehicle collisions by filling in the following (Round your answers to dollars and cents).

a. df =

b. Critical value =

c. Point Estimate =

d. Standard Error of the Estimate = 

BSTA 200 Online Fall 2019

e. Margin of Error =

f. LCL =

UCL =

4. In a survey conducted to determine, among other things, the cost of vacations, 64 individuals were randomly sampled. Each person was asked to compute the cost of his or her most recent vacation. The sample showed a sample mean of $1810. Assuming that the population standard deviation (σ) is $600, construct a 90% confidence interval for the average cost of all vacations by filling in the following.Round your answers to dollars and cents).

a. df =

b. Critical value =

c. Point Estimate =

d. Standard Error of the Estimate =

e. Margin of Error =

f. LCL =

UCL =

5. A car dealership claims that its average service time is less than 7 hours on weekdays. A random sample of 16 service times was recorded and yielded the statistics