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Find the probability of an observation lying more than z = 0.5 standard deviations below the mean.

Toyota would like to know how many miles per gallon the average driver gets when driving the hybrid Toyota Prius.  A random sample of 225 drivers yields a mean of 50 mpg and a standard deviation of 7.5 mpg. Estimate the population mean for the miles per gallon of the Prius using a 90% confidence interval.

Assume that 15% of all pigs die between birth and weaning.  In a random sample of 200 births, let X be the number of pigs that die between birth and weaning.  Using the normal approximation to the binomial, find the approximate probability that the number of pigs in the sample of 200 that die between birth and weaning is greater than or equal to 40.

The mean length of time required to complete a 5K race was 20 minutes.  The standard deviation of the times was 4 minutes.  The racing times were approximately normally distributed.  Only 10% of the runners would be expected to complete the race in less than x minutes.  Find the value of x.

A survey was conducted to determine how people rate the quality of programming available on TV.  Twenty-one respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display based on these data (using the first digit as the stem and the second digit as the leaf) is shown below: Stem                       Leaves                                     3               2     5 4               0     3     4     7     8     9 5               1     1     2     3     4     5 6               1     2     5     6     7 7               7     8 Based on the stem-and-leaf display, the median for these TV ratings is __________.

Find the probability of an observation lying more than z = 2.17 standard deviations above the mean.

A randomized block design is used to compare postweaning average daily gains of 4 breeds of beef cattle, Hereford, Angus, Charolais, and Simmental (we can think of the breeds at the “treatments”).  The breeds are divided into 3 weight classes (i.e., 3 blocks).  Block 1 contains cattle weighing 450 to 500 lb at the beginning of the experiment, block 2 contains cattle weighing 500 to 550 lb at the beginning of the experiment, and block 3 contains cattle weighing 550 to 600 lb at the beginning of the experiment.  The postweaning average daily gains (in pounds per day) are as follows:  Block Hereford Angus Charolais Simmental 1 3.50 3.60 3.70 3.75 2 3.55 3.63 3.71 3.80 3 3.56 3.62 3.80 3.90 The partially completed ANOVA table for this experiment is as follows: Source df SS MS F Total   .160     Breed   .139 .046 46 Block   .014 .007   Error   .007 .001   What are the correct degrees of freedom for total, breed, block, and error, respectively?

The heights of 9 students (in inches) are as follows:  60  62   66   72   74   64   68   69   67 Find the median.

Assume that the mean weight of a sample of calves is 600 lb and the standard deviation of the weights is 50 lb.  If the data set does not have a symmetric and mound shaped distribution, and we therefore use Chebyshev’s Rule, we would expect at least what percent of the calves to have weights between 500 and 700 lb?

The weights of 25 lambs (in pounds) in a flock of sheep are as follows: 68     73     66     76     86     74     61     89     65     90 69     92     76     62     81     63     68     81     70     73     60     87     75     64     82 Construct a stem-and-leaf display using the first digit as the stem and the second digit as the leaf.  Based on the stem-and-leaf display, the lower quartile for this set of weights is __________ lb.