Question

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 choicesBiologyStatisticsBoth 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.

Answer 1

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