The final scores of students in mathematics are distributed normally with a mean of 72 and a standard deviation of 10. What is the probability that a student’s score will be between 65 and 78?.

Answer:

0.8041

Explanation:

0.8041

We know that  

μ=72  and  σ=5

and P(65<X<78)

We can determine the Z value as (X-μ)/σ

P( 65<X<78 )=P( 65-72< X-μ<78-72)

P((65-72)/5 < Z < (78-72)/5)P((65−72)/5<Z<(78−72)/5)

P(65 < X < 78 )=P(-1.4 < Z < 1.2)P(65<X<78)=P(−1.4<Z<1.2)

To fine the Z values:

P (-1.4 < Z < 1.2 )=P ( Z < 1.2 )-P (Z < -1.4 )P(−1.4<Z<1.2)=P(Z<1.2)−P(Z<−1.4)

From the standard normal tables:

P (Z < 1.2 )=0.8849P(Z<1.2)=0.8849

to find P ( Z<-1.4)

P ( Z < -a)=1-P ( Z < a )P(Z<−a)=1−P(Z<a)

From the standard normal tables:

P ( Z < -1.4)=1-P ( Z < 1.4 )=1-0.9192=0.0808P(Z<−1.4)=1−P(Z<1.4)=1−0.9192=0.0808

Therefore

P(-1.4 < Z < 1.2 )=0.8041P(−1.4<Z<1.2)=0.8041

P (65 < X < 78)=0.8041P(65<X<78)=0.8041

A botanist found a correlation between the length of an aspen leaf and its surface area to be 0. 94. Why does the correlation value of 0. 94 not necessarily indicate that a linear model is the most appropriate model for the relationship between length of an aspen leaf and its surface area?.

On your property tax bill, you see the following table. Destination Share of Your Taxes Roads $241 Schools $896 Public Safety $154 Township $177 What percentage of your taxes went to funding public safety? a. 10. 49% b. 12. 06% c. 11. 72% d. 8. 94% Please select the best answer from the choices provided A B C D.

Which timeline shows the correct order of contributions made to the discovery of dna?.

Why did mirabeau b. Lamar easily win the presidency in 1838.

Explain how biology can be studied from a microscopic.