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Chapter 6: Q. 78 (page 358)
Long or short? Put the names of all the students in your statistics class in a hat. Mix up the names, and draw 4 without looking. Let X = the number whose last names have more than six letters.
The given statement is correct, is based on the binomial distribution.
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Housing in San José How do rented housing units differ from units occupied by their owners? Here are the distributions of the number of rooms for owner-occupied units and renter-occupied units in San José, California:
Let X= the number of rooms in a randomly selected owner-occupied unit and Y = the number of rooms in a randomly chosen renter-occupied unit.
(a) Here are histograms comparing the probability distributions of X and Y. Describe any differences you observe.
(b) Find the expected number of rooms for both types of housing unit. Explain why this difference makes sense.
(c) The standard deviations of the two random variables are and . Explain why this difference makes sense.
In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p ?
a.
b.
c.
d.
e.
Baby elk Biologists estimate that a randomly selected baby elk has a 44 % chance of surviving to adulthood. Assume this estimate is correct. Suppose researchers choose 7 baby elk at random to monitor. Let X= the number that survive to adulthood.
Swim team Hanover High School has the best women's swimming team in the region. The meter freestyle relay team is undefeated this year. In the -meter freestyle relay, each swimmer swims meters. The times, in seconds, for the four swimmers this season are approximately Normally distributed with means and standard deviations as shown. Assuming that the swimmer's individual times are independent, find the probability that the total team time in the meter freestyle relay is less than seconds.follow the four step process.
| Swimmer | Mean | Std.dev |
| Wendy | 55.2 | 2.8 |
| Jill | 58.0 | 3.0 |
| Carmen | 56.3 | 2.6 |
| Latrice | 54.7 | 2.7 |
During the winter months, the temperatures at the Starneses’ Colorado cabin can stay well below freezing for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes sets the thermostat at She also buys a digital thermometer that records the indoor temperature each night at midnight. Unfortunately, the thermometer is programmed to measure the temperature in degrees Celsius. Based on several years’ worth of data, the temperature in the cabin at midnight on a randomly selected night can be modeled by a Normal distribution with mean and standard deviation . Let the temperature in the cabin at midnight on a randomly selected night in degrees Fahrenheit (recall that.
a. Find the mean of .
b. Calculate and interpret the standard deviation of
c. Find the probability that the midnight temperature in the cabin is less than .
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