1.) On the distant planet Cowabunga, the weights of cows have a normal distribution with a mean of 547 pounds and a standard deviation of 71 pounds. The cow transport truck holds 14 cows and can hold a maximum weight of 7882. If 14 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 7882? (This is the same as asking what is the probability that their mean weight is over 563.)(Give answer correct to at least three decimal places.)
probability =
Box 1: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity
2.) The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.2 years and a standard deviation of 0.6 years. He then randomly selects records on 34 laptops sold in the past and finds that the mean replacement time is 2.9 years.
Assuming that the laptop replacement times have a mean of 3.2 years and a standard deviation of 0.6 years, find the probability that 34 randomly selected laptops will have a mean replacement time of 2.9 years or less.
P(M < 2.9 years) =
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Based on the result above, does it appear that the computer store has been given laptops of lower than average quality?
- No. The probability of obtaining this data is high enough to have been a chance occurrence.
- Yes. The probability of this data is unlikely to have occurred by chance alone
3.) The lengths of pregnancies in a small rural village are normally distributed with a mean of 268 days and a standard deviation of 12 days.
In what range would you expect to find the middle 50% of most pregnancies?
Between___ and___ .
If you were to draw samples of size 45 from this population, in what range would you expect to find the middle 50% of most averages for the lengths of pregnancies in the sample?
Between___ and___ .
Enter your answers as numbers. Your answers should be accurate to 1 decimal places.
4.) A population of values has a normal distribution with μ=159.μ=159.4 and σ=80.5 σ=80.5 You intend to draw a random sample of size n=25 n=25
Find the probability that a single randomly selected value is greater than 114.3.
P(X > 114.3) =
Find the probability that a sample of size n=2 n=25 is randomly selected with a mean greater than 114.3.
P(M > 114.3) =
Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.