7.1 the standard normal distribution

Question 1

probability density of the random vairable

Answer 1

curve that decribes the distribution of a variable

Question 2

normal curve, normally distributed, normal distribution

Answer 2

has one peak and its in the middle

Question 3

properties of a normal curve

Answer 3

mean and median of a normal distribution are equal and they are both equal to the mode. wide and flat when the population standard deviation is large, tall and narrow when the population standard deviation is small

Question 4

standardization, converting x to a z-score for an x value from a normal distrubtion

Answer 4

z=(x-(the mean))/standard deviation

Question 5

standard normal distribution

Answer 5

normal distribution with a mean of 0 and standard deviation of 1

Question 6

properties of normal distributions

Answer 6

1.normal distributions have one mode 2.normal distributions are symmetric around the mode 3. the mean and median of a normal distribution are both equal to the mode. in other words, the mean, median and mode of a normal distrubution are all the same. 4. the normal distribution follows the emerical rule

Question 7

find are between two z-scores using the ti-84 plus calc

Answer 7

find area between z=-1.45 and z=.42
2nd, vars, normalcdf command, lower:-1.45, upper: .42, mean:0, standard deviation:1, make sure to close parentheses
area=.589228

Question 8

find a z-score corresponding to the area 0.26 using the ti-84 plus calc
note: the mode, z=0 has an area of 0.5 both to its right and its left

Answer 8

2nd, vars, invNorm, area:0.26, mean:0, standard deviation:1, make sure to close parentheses
area=-.6433

Question 9

=invNorm(area, mean, standard deviation)

for z scores

Answer 9

area= given area to the left
mean=0
standard deviation=1

Question 10

find the z-scores that bound the middle 95% of the area under the standard normal curve

Answer 10

1. the entire area under the curve should equal 1, therefore the remaining area to left and right of the 95% middle area is 0.025 each
2. input (0.025, 0, 1) in invNorm
   this equals -1.959964
3. knowing the area to the right of the middle area is 0.025, meaning the rest altogether to its left is 0.975, therefore invNorm(0.975, 0, 1)= 1.959964
   4, therefore the areas that bound the middle area is -1.96 and 1.96