Question

Given a normal distribution with mean of 100 and standard deviation of 10, what is the...

Given a normal distribution with mean of 100 and standard deviation of 10, what is the probability that:

a. X > 80?

b. X < 65?

c. X < 75 or X > 90?

d. Between what two X values (symmetrically distributed around the mean) are ninety percent of the values

Homework Answers

Answer #1

a.

X ~ N(100, 102)

P(X > 80) = P[Z > (80 - 100)/10] = P[Z > -2] = 0.9772

b.

P(X < 65) = P[Z < (65 - 100)/10] = P[Z < -3.5] = 0.0002

c.

P(X < 75 or X > 90) = P(X < 75) + P(X > 90)

= P[Z < (75 - 100)/10] + P[Z > (90 - 100)/10]

= P[Z < -2.5] + P[Z > -1]

= 0.0062 + 0.8413

= 0.8475

d.

For ninety percent of the values, the percentiles are (1 - 0.9)/2 and 0.9 + (1 - 0.9)/2 which are  0.05 and 0.95

Z value for p = 0.05 and 0.95 are -1.645 and 1.645

The two values are,

100 - 1.645 * 10 = 83.55

100 + 1.645 * 10 = 116.45

Between 83.55 and 116.45, 90% of the data lies.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

ADVERTISEMENT