Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

BIOSTATS > NORMAL DISTRIBUTION > Flashcards

NORMAL DISTRIBUTION Flashcards

1
Q

symmetric distribution where the data values are evenly distributed about

A

mean

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

what is the shape of the normal distribution

A

Bell-shaped

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

It is the other term for the normal distribution

A

Gaussian Distribution

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

it is an important assumption in parametric test

A

Normal Distribution

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

In the normal distribution Mean, median, and mode are essentially___________

A

the same

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

not symmetric and extends more to one side than the other

A

Skewed

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Left skewed is aka

A

negatively skewed

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

order of mean, median, mode in left- skewed

A

mean

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

order of mean, median, mode in right- skewed

A

mean>median>mode

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

A normal distribution can have any ______and any______________

A

mean and positive standard

deviation.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

describes the spread of the data.

A

standard deviation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

The higher the
standard deviation, the ________ the values are from
the mean.

A

more it is spread or the farther

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

if the __________ is increased the spread of

the data will increase also.

A

standard deviation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

relationship of mean, median, and mode in normal distribution

A

they are equal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

The normal curve is

shaped like a ________and symmetric about the_______

A

bell; mean.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

The total area under the curve is equal to__

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

The normal curve approaches, but never touches the________as it extends
farther and farther away from the ________(Asymptotic)

A

x-axis; mean.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

the number of standard deviations that a given x value is above or below
the mean

A

zScore

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

Non-standard /General Distribution

A

Left curve

20
Q

Standard Normal Distribution

A

Right Curve

21
Q

Standard Normal Distribution - the Mean is always __ and

standard deviation is always _____. Regardless the range of X values.

A

zero; one

22
Q

P(X) and P(Z) corresponds to the area under the curve which is ____

A

one (1)

23
Q

range of the Probability for a given value: _______________

A

0 ≤ P (Z) ≤ 1

24
Q

Total percentage of the values is____ Positive infinity to negative
infinity is ____

A

100%

25
Q

Empirical Rule: 1 standard deviation=___

A

68%

26
Q

Empirical Rule: 2 standard deviation=___

A

95%

27
Q

Empirical Rule: 3 standard deviation=___

A

99.7%

28
Q

Calculating the z score given the area or probability.

A

(Reverse lookup

process)

29
Q

First thing to do in finding the area or probability given an x value.

A

Convert x to z: Standardized first using the formula: z = x - µ / σ

30
Q

find P (z≤ - 1.61) in percentage

A

5.37%

31
Q

find P(z≤1.5) in percentage

A

93.32%

32
Q

P (z ≤ -1.56)

A

0.0594

33
Q 
The final exam scores in a statistics class were normally distributed 
with a mean of 63 and a standard deviation of 5. Find the probability that a 
randomly selected student scored less than 65 on the exam.... what is the z-score?
A

0.4

34
Q 
The final exam scores in a statistics class were normally distributed 
with a mean of 63 and a standard deviation of 5. Find the probability that a 
randomly selected student scored less than 65 on the exam.
A 
µ= 63; x = 65. σ =5
• P (x ≤ 65)
• z=x- µ/σ = 65-63/5 = 0.4
• P (z ≤ 0.4) = 0.6554
• Ans: The probability is 65.54%
35
Q

What is the probability of getting a standard normal value greater than
0.93?

A

P (z ≥ 0.93) = 0.8238 (area not shaded)
1-0.8238= 0.1762 (area shaded: looking for)
Ans: 17.62%

36
Q

Rule for probability of complements

A

1 - P (z ≤ z)

37
Q

The final exam scores in a statistics class were normally distributed
with a mean of 63 and a standard deviation of 5. Find the probability that a
randomly selected student scored more than 57 on the exam.
• The question is the blue shaded part

A
  • The question is the blue shaded part.
  • µ=63; x=57. σ =5
  • P(x57): convert x to z
  • z=x- µ/σ =57-63/5 =-1.2
  • P (z ≤ -1.2) = 0.1151
  • 1- P (z ≤ -1.2) = 1-0.1151 = 0.8849.
  • Ans: the probability is 88.49%
38
Q

Find the area under the standard normal curve between z =- 1.98 and
z= 1.07

A 
• P (-1.98 ≤ z ≤ 1.07) 
• P (z ≤ 1.07) = 0.8577
• P (z ≥ -1.98)= 0.0239
• Area of the shaded part: 0.8577 - 0.0239 = 0.8338
→ Ans: 0.8338
39
Q

The systolic blood pressure (SBP) of adult men is normally distributed
with mean of 110 mmHg and standard deviation of 15 mmHg. How many
percent of adult men have systolic blood pressures between 90 mmHg and 125
mmHg?

A 
• µ=110; 90 ≤ x ≤ 125; =15
• 1st: convert x to z
→ P (x ≤ 125) = 125-110/ 15 = 1
→ P (x ≥ 90) = 90-110/ 15 = -1.33
• Z-score:
→ P (z ≤ 1) = 0.8413
→ P (z ≥ -1.33) = 0.0918
• Area between the 2 z-scores: 
→ 0.8413-0.0918= 0.7495
→ ANS: 74.95%
40
Q 
The final exam scores in a statistics class were normally distributed 
with a mean of 63 and a standard deviation of 5. Find the probability that a 
randomly selected student scored between 55 and 70.
A 
• µ=63; 55 ≤ x ≤ 70; =5
• 1st: convert x to z
→ P (x ≤ 70) = 70-63/ 5 = 1.4
→ P (x ≥ 55) = 55-63/ 5 = -1.6
• Z-score:
→ P (z ≤ 1.4) = 0.9192
→ P (z ≥ -1.6) = 0.0548
• Area between the 2 z-scores: 0.9192-0.0548= 0.8644
→ ANS: 86.44%
41
Q

Find the value of z1 in the figure below. The area to the left of z1 is 0.0485 or
P(z

A

Find the value of z2= 0.9224

42
Q

Find the z-score above which lies 20% of scores in the normal distribution

A

→ Want to find the z-score that cuts the distribution into lower 80% and
upper 20%
→ Same as 80th percentile
→ Closest to the given area 0.8 is 0.7995
→ ANS: 0.84

43
Q

Find the z-score that corresponds to P75.

A

Ask about the z score that cuts the distribution to lower 75% and upper
25%.
→ Area= 0.75; P75: lower 75%
→ 0.75: z-score = closest 0.7486 which is 0.67

44
Q

Find x1 such that P (X

A

→ 0.9332 in z-score is 1.5
→ x=10+1.5(2.5) = 13.75
→ 1.5 above the mean

45
Q

Find x1 such that P (X >x1) = 0.65, where X is a normal random variable with
μ = 175 and σ = 12

A

→ Determine the area to the left: 1- P(xx1) = 1- 0.65 = 0.35
→ 0.35 in z-score is -0.39 (.3483)
→ x=175+(-.39) (12) =170.32
→ x1=170.32 and located -.39 below the mean.

46
Q

X is a normally distributed random variable with mean of 15 and standard
deviation of 0.25. Find the values x1 and x2 that are symmetrically located
with respect to the mean of X and satisfy P(x1

A

→ Areas to the right and to left of the shaded area have a value of 0.1
▪ Determine the z2:
→ Area = 0.9 -> (0.8: shaded area plus 0.1: left side of the shaded area)
▪ Determine the z1:
→ Area= 0.1 the left side area
▪ In the z-table: z2 =1.28 (0.8997)
▪ z1=-1.28 (0.1003)

Symmetric
→ x2, =15+1.28(0.25) =15.32
→ x1, =15+(-1.28) (0.25) =14.68
→ x1=14.68; x2=15.32 and x2 located 1.28 above the mean while x1 located 
-1.28 below the mean

BIOSTATS (4 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions