The scores received by juniors on the math portion of the PSAT are normally distributed with a mean of 48.6 and a standard deviation of 11.4. What is the probability that a randomly selected score is at least 76?

0.82%

Step-by-step explanation:

We have that the mean (m) is equal to 48.6, the standard deviation (sd) 11.4

They ask us for P (x >76)

For this, the first thing is to calculate z, which is given by the following equation:

z = (x - m) / sd

We have all these values, replacing we have:

z = (76 - 48.6) / (11.4)

z = 2.4

With the normal distribution table (attached), we have that at that value, the probability is:

P (z <2.4) = 0.9918

Thus:

P (x> 76) = 1 - P (x <76)

P (x> 76) = 1 - 0.9918 = 0.0082

It means that the probability is 0.82%

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500