Question

A day care program has an average daily expense of $75.00. the standard deviation is $5.00. the owner takes a sample of 64 bills. what is the probability the mean of his sample will be between $70.00 and $80.00? step 1. calculate a z-score for $70.00 - step 2. give the probability for step 1. % step 3. calculate the z-score for $80.00 step 4. give the probability for step 3. % step 5. add the probabilities from steps 2

Answer 1

B. 68

Explanation:

x is a raw score to be standardized;

μ is the mean of the population;

σ is the standard deviation of the population.

Therefore the mean is zero. Seventy is -1z, or -1 standard deviation.

Step 2: 34.13% of the cases fall between -1 standard deviation and the mean. Thus there is a 34.13% chance that the score will fall between 70 and 75. This, of course, assumes a normal curve.

Step 3: An 80 is +1z or +1 standard deviation assuming a normal curve.

Step 4: Thirty four percent of the cases fall between +1 standard deviation and the mean. Thus there is a 34.13% chance that the score will fall between 75 and 80. This, of course, assumes a normal curve.

Step 5: Score between +1z and -1z, or +1 and -1 standard deviation account for 68.26% of the cases.