Q1.

What requirements are necessary for a normal probability distribution to be a *standard* normal probability distribution?

Choose the correct answer below.

A. The mean and standard deviation have the values of

mu equals 1μ=1

and sigma equals 1.σ=1.

B. The mean and standard deviation have the values of

mu equals 0μ=0

and sigma equals 1.σ=1.

Your answer is correct.

C. The mean and standard deviation have the values of

mu equals 1μ=1

and sigma equals 0.σ=0.

D. The mean and standard deviation have the values of

mu equals 0μ=0

and sigma equals 0.

Q2

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Click to view page 1 of the table. z equals 0.32 A graph with a bell-shaped curve, divided into 2 regions by a line from top to bottom on the right side. The region left of the line is shaded. The z-axis below the line is labeled "z=0.32". The area of the shaded region is 0.6255. (Round to four decimal places as needed.)

Q3

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.

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1

Q4

Assume that thermometer readings are normally distributed with a mean of

0degrees°C and a standard deviation of 1.00degrees°C.

A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in Celsius degrees.)

Assume the readings on thermometers are normally distributed with a mean of

0degrees°C and a standard deviation of 1.00degrees°C.

Find the probability that a randomly selected thermometer reads between negative 1.13−1.13

and negative 0.29−0.29 and draw a sketch of the region

Q5

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

negative 1.81−1.81 and 1.811.81.

Q6

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 3.67and draw a sketch of the region.

Q7

Assume that the readings on the thermometers are normally distributed with a mean of

0 degrees0° and standard deviation of 1.00degrees°C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to Upper P 88P88, the

88 thThis is the temperature reading separating the bottom 88% from the top 12 %.

Assume that the readings on the thermometers are normally distributed with a mean of

0 degrees0° and standard deviation of 1.00degrees°C. Assume 2.82.8% of the thermometers are rejected because they have readings that are too high and another 2.82.8% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.

Q8

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 99% and highest 99%,

indicating levels that are too low or too high, respectively.

Assume that adults have IQ scores that are normally distributed with a mean of

96.796.7 and a standard deviation of 18.418.4. Find the probability that a randomly selected adult has an IQ greater than

125.3125.3. (Hint: Draw a graph.)

Q9

Engineers want to design seats in commercial aircraft so that they are wide enough to fit

9595% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of

14.814.8 in. and a standard deviation of 1.11.1 in. Find Upper P 95P95. That is, find the hip breadth for men that separates the smallest 9595% from the largest 55%.

Q10

Assume that adults have IQ scores that are normally distributed with a mean of

96.596.5 and a standard deviation 16.316.3. Find the first quartile Upper Q 1Q1,

which is the IQ score separating the bottom 25% from the top 75%. (Hint: Draw a graph.)

Q11

A survey found that women's heights are normally distributed with mean

63.863.8 in and standard deviation 2.42.4 in. A branch of the military requires women's heights to be between 58 in and 80 in.

- Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?
- If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?
- The percentage of women who meet the height requirement is

(Round to two decimal places as needed.)

Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?

A. No, because only a small percentage of women are not allowed to join this branch of the military because of their height.

B. No, because the percentage of women who meet the height requirement is fairly small.

C. Yes, because the percentage of women who meet the height requirement is fairly large.

D. Yes, because a large percentage of women are not allowed to join this branch of the military because of their height.

For the new height requirements, this branch of the military requires women's heights to be at least in.

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