Question

In: Statistics and Probability

CNNBC recently reported that the mean annual cost of auto insurance is 975 dollars. Assume the...

CNNBC recently reported that the mean annual cost of auto insurance is 975 dollars. Assume the standard deviation is 262 dollars, and the cost is normally distributed. You take a simple random sample of 37 auto insurance policies. Round your answers to 4 decimal places.

What is the distribution of XX? XX ~ N(,)

What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)

What is the probability that one randomly selected auto insurance is more than $937?

a simple random sample of 37 auto insurance policies, find the probability that the average cost is more than $937.

For part d), is the assumption of normal necessary? YesNo

Solutions

Expert Solution

Solution :

Given that,

mean = = 975

standard deviation = = 262

a.

X N (975 , 262)

b.

n = 37

= 975

= / n = 262 / 37 = 43.0725

N (975 , 43.0725)

c.

P(x > $937) = 1 - P(x < 937)

= 1 - P[(x - ) / < (937 - 975) / 262)

= 1 - P(z < -0.15)

= 1 - 0.4404

= 0.5596

Probability = 0.5596

d.

P( > $937) = 1 - P( < 937)

= 1 - P[( - ) / < (937 - 975) / 43.0725]

= 1 - P(z < -0.88)

= 1 - 0.1894

= 0.8106

Probability = 0.8106

For part d)

Yes


Related Solutions

CNNBC recently reported that the mean annual cost of auto insurance is 1002 dollars. Assume the...
CNNBC recently reported that the mean annual cost of auto insurance is 1002 dollars. Assume the standard deviation is 214 dollars, and the cost is normally distributed. You take a simple random sample of 18 auto insurance policies. Round your answers to 4 decimal places. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the probability that one randomly selected auto insurance is less than $1042? a simple random...
CNNBC recently reported that the mean annual cost of auto insurance is 966 dollars. Assume the...
CNNBC recently reported that the mean annual cost of auto insurance is 966 dollars. Assume the standard deviation is 244 dollars, and the cost is normally distributed. You take a simple random sample of 38 auto insurance policies. Round your answers to 4 decimal places. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the probability that one randomly selected auto insurance is more than $919? a simple random...
CNNBC recently reported that the mean annual cost of auto insurance is 999 dollars. Assume the...
CNNBC recently reported that the mean annual cost of auto insurance is 999 dollars. Assume the standard deviation is 299 dollars. You take a simple random sample of 67 auto insurance policies. Find the probability that a single randomly selected value is at least 963 dollars. P(X > 963) = Find the probability that a sample of size n = 67 is randomly selected with a mean that is at least 963 dollars. P(M > 963) =
CNNBC recently reported that the mean annual cost of auto insurance is 1004 dollars. Assume the...
CNNBC recently reported that the mean annual cost of auto insurance is 1004 dollars. Assume the standard deviation is 278 dollars. You take a simple random sample of 55 auto insurance policies. Find the probability that a single randomly selected value is less than 997 dollars. P(X < 997) = Find the probability that a sample of size n = 55 is randomly selected with a mean less than 997 dollars. P( ¯ x < 997) =
CNNBC recently reported that the mean annual cost of auto insurance is 1008 dollars. Assume the...
CNNBC recently reported that the mean annual cost of auto insurance is 1008 dollars. Assume the standard deviation is 299 dollars. You take a simple random sample of 58 auto insurance policies. Find the probability that a single randomly selected value is more than 961 dollars. P(X > 961) = Find the probability that a sample of size n = 58 is randomly selected with a mean that is more than 961 dollars. P(M > 961) =
CNNBC recently reported that the mean annual cost of auto insurance is 978 dollars. Assume the...
CNNBC recently reported that the mean annual cost of auto insurance is 978 dollars. Assume the standard deviation is 299 dollars. You take a simple random sample of 92 auto insurance policies. Find the probability that a single randomly selected value is less than 988 dollars. P(X < 988) = ___________ Find the probability that a sample of size n=92n=92 is randomly selected with a mean less than 988 dollars. P(M < 988) = ____________
CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the...
CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 213 dollars. You take a simple random sample of 87 auto insurance policies. Find the probability that a single randomly selected value exceeds 1000 dollars. P(X > 1000) = Find the probability that a sample of size n = 87 is randomly selected with a mean that exceeds 1000 dollars. P(M > 1000) = Enter your answers as numbers accurate to...
CNNBC recently reported that the mean annual cost of auto insurance is 960 dollars. Assume the...
CNNBC recently reported that the mean annual cost of auto insurance is 960 dollars. Assume the standard deviation is 194 dollars. You will use a simple random sample of 101 auto insurance policies. Find the probability that a single randomly selected policy has a mean value between 927.2 and 1016 dollars. P(927.2 < X < 1016) = Find the probability that a random sample of size n=101n=101 has a mean value between 927.2 and 1016 dollars. P(927.2 < M <...
CNNBC recently reported that the mean annual cost of auto insurance is 1035 dollars. Assume the...
CNNBC recently reported that the mean annual cost of auto insurance is 1035 dollars. Assume the standard deviation is 275 dollars. You take a simple random sample of 54 auto insurance policies. Find the probability that a sample of size n=54 is randomly selected with a mean less than 989 dollars. P(M < 989) =
CNNBC recently reported that the mean annual cost of auto insurance is 989 dollars. Assume the...
CNNBC recently reported that the mean annual cost of auto insurance is 989 dollars. Assume the standard deviation is 294 dollars. You take a simple random sample of 75 auto insurance policies. Find the probability that a single randomly selected value is less than 979 dollars. P(X < 979) = Find the probability that a sample of size n = 75 is randomly selected with a mean less than 979 dollars. P(M < 979) = Enter your answers as numbers...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT