Chapter 6-1:

Find the indicated area under the curve of the standard normal​ distribution; then convert it to a percentage and fill in the blank. About _____% of the area is between z=-3.5 and z=3.5

About _99.95_% of the area is between z=-3.5 and z=3.5 normalcdf(-3.5,3.5,0,1)=0.9995x100=99.95%

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. z=-0.91 z=1.26 The area of the shaded region is _____.

The area of the shaded region is _0.7148_. normalcdf(-0.91,1.26,0,1)=0.7148

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. z=-1.04 The area of the shaded region is _____.

The area of the shaded region is _0.8508_. normalcdf(-1.04,10000,0,1)=0.8508

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Area: 0.3050 The indicated z score is _____.

The indicated z score is _-0.51_. invNorm(0.3050,0,1,LEFT)=-0.51

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. area=0.7995 The indicated z score is _____.

The indicated z score is _-0.84_. invNorm(0.7995,0,1,RIGHT)=-0.84

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. area=0.1446 The indicated z score is _____.

The indicated z score is _1.06_. invNorm(0.1446,0,1,RIGHT)=1.06

The notation P(z<a) denotes __________.

The notation P(z<a) denotes _the probability that the z-score is less than a._

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than -1.66 and draw a sketch of the region. The probability is ______.

The probability is _0.0485_. normalcdf(-10000,-1.66,0,1)=0.0485

Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between -1.82 and -1.04 and draw a sketch of the region. The probability is ______.

The probability is _0.1148_. normalcdf(-1.82,-1.04,0,1)=0.1148

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score greater than 0.32. The probability is _____.

The probability is _0.3745_. normalcdf(0.32,10000,0,1)=0.3745

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score less than 0. The probability is ______.

The probability is _0.5000_. normalcdf(-10000,0,0,1)=0.5000

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score greater than 0. The probability is ______.

The probability is _0.5000_. normalcdf(0,10000,0,1)=0.5000

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score greater than -1.52. The probability is _____.

The probability is _0.9357_. normalcdf(-1.52,10000,0,1)=0.9357

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score between -2.17 and 2.17. The probability is _____.

The probability is _0.9700_. normalcdf(-2.17,2.17,0,1)=0.9700

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than 2.03 and draw a sketch of the region. The probability is _____.

The probability is _0.9788_. normalcdf(-10000,2.03,0,1)=0.9788

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is between -2.06 and 3.74 and draw a sketch of the region. The probability is _____.

The probability is _0.9802_. normalcdf(-2.06,3.74,0,1)=0.9802

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 60.0 minutes. Find the probability that a given class period runs between 50.5 and 51.0 minutes. Find the probability of selecting a class that runs between 50.5 and 51.0 minutes. _____

Find the probability of selecting a class that runs between 50.5 and 51.0 minutes. _0.05_ 60-50=10=1/10 51-50.5=0.5 0.5*1/10=0.05

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes. _____

Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes. _0.750_ (9-2.25)/(9-0)=0.750

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the bone density test scores that can be used as cutoff values separating the lowest 9% and highest 9%, indicating levels that are too low or too​ high, respectively. The bone density scores are _____.

The bone density scores are _-1.34,1.34_. invNorm(0.09,0,1,LEFT)=-1.34 invNorm(0.09,0,1,RIGHT)=1.34

What does the notation z(alpha) indicate? The expression z(alpha) denotes the z score with an area of (alpha) __________.

The expression z(alpha) denotes the z score with an area of (alpha) _to its right_.

Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. Between 0.50 and 1.25 The probability of getting a reading between 0.50°C and 1.25°C is ______.

The probability of getting a reading between 0.50°C and 1.25°C is _0.2029_. normalcdf(0.50,1.25,0,1)=0.2029

For bone density that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are a) The percentage of bone density scores that are significantly high is ______. b) The percentage of bone density scores that are significantly low is ______. c) The percentage of bone density scores that are not significant is ______.

a) The percentage of bone density scores that are significantly high is _2.28_. b) The percentage of bone density scores that are significantly low is _2.28_. c) The percentage of bone density scores that are not significant is _95.44_.

Which of the following groups of terms can be used interchangeably when working with normal​ distributions? a) areas, probability, and relative frequencies b) areas, z-scores, and probability c) areas, z-scores, and relative frequencies d) z-scores, probability, and relative frequencies

a) areas, probability, and relative frequencies

What requirements are necessary for a normal probability distribution to be a standard normal probability distribution? a) The mean and standard deviation have the values of u=1 and o=1 b) The mean and standard deviation have the values of u=0 and o=0 c) The mean and standard deviation have the values of u=0 and o=1 d) The mean and standard deviation have the values of u=1 and o=0

c) The mean and standard deviation have the values of u=0 and o=1