We want to compare the grades on an introductory biology exam (100 points total) for freshman versus sophomores. Suppose that 68% percent of the class are freshman, while the remaining are sophomores. The exam grades for freshman were normally distributed, with a mean of 84 and a standard deviation of 15. The exam grades for sophomores were also normally distributed, and 40% of the entire class got an "A" on the test (scored at least 90)

a. Students who did better than 80% of the freshman in the class got at least what grade?

b. What proportion of freshman got a "B" on the test (scored between 80 and 90)?

c. What proportion of sophomores got an "A" on the test?

d. If the standard deviation of exam grades for sophomores is the same as it is for freshman, what is the mean sophomore grade on the exam?

a)

b) P(80<x<90)=0.6554-0.3949=0.2606

c) P(A | sophomores)=0.5178

d) μ=90.67

Step-by-step explanation:

a)

Step 1:   establish the  inequality

P(x<xL)=0.8, where x= random variable

Step 2:  standardization

μ)/σ=(-84)/15

Step 3: Find z in z-table

Step 4:

(-84)/15=0.8416 ->

b)

Step 1:   establish the  inequality

P(80<x<90)

Step 2:  standardization

z=(80-84)/15= -0.2667

z=(90-84)/15= 0.4

Step 3: simplify

P(80<x<90)=P( -0.2667<z<0.4)=P(z<0.4)-P(z<-0.2667)

Step 4: look for probability in z-table

P(80<x<90)=0.6554-0.3949=0.2606

c) total probability theorem

P(A)=P(A∩freshman)+P(A∩sophomores)=P(A | freshman)*P(freshman)+P(A | sophomores)*P(sophomores)=P(x>90)*0.68+P(A | sophomores)*(1-0.68)=(1-0.6554)*0.68+P(A | sophomores)*0.32=0.4

then

P(A | sophomores)=0.5178

d)

Step 1:   establish the  inequality

P(y>90)=0.5178, where y= random variable

Step 2:  standardization

z=(y-μ)/σ=(90-μ)/15

Step 3: Find z in z-table

Step 4:

(90-μ)/15=-0.0446 ->μ=90.67

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x