probability

1. A normal population had a mean of 60 and a standard deviation of 12.
A random sample of 36 units is drawn from the population. Find:
a) The standard error of the mean.
b) The probability that the sample mean is less than 62.
c) The probability that the sample mean is between 58 and 61.
d) The probabilty that the samp[le mean is between 56 and 59.

2. A random sample of 25 apples were take from a large apple tree and were weighted.
The mean weight of an apple in the sample was found to be 8 oz.
The weights of apples in the tree were known to be normally distributed with a standard
deviation of 1.5 oz. Find:
a) The 90% confidence interval for the population mean.
b) The 95% confidence interval for the population mean.

3. A random sample of 16 workers in large factory had an average hourly rate of $10.
The nsample standard deviation was $2.
The hourly rates of workers in the factory is assumed to be normally distributed.
Using Student t Distribution find:
a) The 90% confidence interval for the population mean.
b) The 95% confidence interval for the population mean.

4. In a random sample of 100 customers in a store 60 customers paid their
bills with credit cards. Find:
a) A point estimate of the proportion of all customers at the store who pay with
credit cards.