The mean speed of vehicles along a stretch of highway is 75 miles per hour with a standard deviation of 3.8 miles per hour. your current speed along this stretch of highway is 62 miles per hour. what is the z-score for your speed? z- score = (round to two decimal places) flag this questionquestion 23 ptsfor a statistics test the mean is 63 and the standard deviation is 7.0, and for a biology test the mean is 23 and the standard deviation is 3.9. a student gets a 60 on the statistics test and a 22 on the biology test, on which of the two tests the student perform better? group of answer are equal flag this questionquestion 321 ptsintelligence quotients (iq scores) are normally distributed with a mean of 100 and a standard deviation of 15. an individual is selected at random, determine the probability that the individual has iq scores. round all answers to 4 decimal places. a) below 90. b) above 130. c) between 90 and 130.

Step-by-step explanation:

) Assuming speed of vehicles along a stretch of highway is normally distributed, the normal distribution formula would be applied. It is expressed as

z = (x - u)/s

Where

x = speed of vehicles

u = mean speed

s = standard deviation

From the information given,

u = 75

s = 3.8

z = (62 - 75)/3.8 = - 3.42

2)the student performed better in the biology test because the spread of the scores is not wide and the student got just 1 below the mean.

3) Since the Intelligence quotients are normally distributed, the normal distribution formula would be applied. It is expressed as

z = (x - u)/s

From the information given,

u = 100

s = 15

a) Below 90

z = (90 - 100)/15 = - 0.67

From the normal distribution table, the corresponding probability is

0.2514

b) Above 130

z = (130 - 100)/15 = 2

From the normal distribution table, the corresponding probability is

0.9773. Therefore,

P(x greater than 130) = 1 - 0.9773 = 0.0227

c) Between 90 and 130. The probability would be

0.9773 - 0.2514 = 0.7259

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm