An image-encoding algorithm, when used to encode images of a certain size, uses a mean of 110 milliseconds with a standard deviation of 15 milliseconds. What is the probability that the mean time (in milliseconds) for encoding 50 randomly selected images of this size will be between 90 milliseconds and 135 milliseconds? What assumptions do we need to make?

"Never Gonna Give You Up"

We're no strangers to love

You know the rules and so do I

A full commitment's what I'm thinking of

You wouldn't get this from any other guy

I just wanna tell you how I'm feeling

Gotta make you understand

Never gonna give you up

Never gonna let you down

Never gonna run around and desert you

Never gonna make you cry

Never gonna say goodbye

Never gonna tell a lie and hurt you

We've known each other for so long

Your heart's been aching, but

You're too shy to say it

Inside, we both know what's been going on

We know the game and we're gonna play it

And if you ask me how I'm feeling

Don't tell me you're too blind to see

Never gonna give you up

Never gonna let you down

Never gonna run around and desert you

Never gonna make you cry

Never gonna say goodbye

Never gonna tell a lie and hurt you

Never gonna give you up

Never gonna let you down

Never gonna run around and desert you

Never gonna make you cry

Never gonna say goodbye

Never gonna tell a lie and hurt you

(Ooh, give you up)

(Ooh, give you up)

Never gonna give, never gonna give

(Give you up)

Never gonna give, never gonna give

(Give you up)

We've known each other for so long

Your heart's been aching, but

You're too shy to say it

Inside, we both know what's been going on

We know the game and we're gonna play it

I just wanna tell you how I'm feeling

Gotta make you understand

Never gonna give you up

Never gonna let you down

Never gonna run around and desert you

Never gonna make you cry

Never gonna say goodbye

Never gonna tell a lie and hurt you

Never gonna give you up

Never gonna let you down

Never gonna run around and desert you

Never gonna make you cry

Never gonna say goodbye

Never gonna tell a lie and hurt you

Never gonna give you up

Never gonna let you down

Never gonna run around and desert you

Never gonna make you cry

Never gonna say goodbye

Never gonna tell a lie and hurt you

you just got rick roll

take it another

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: