Question

Daily sales of bagels at a local bakery is a random variable normally distributed with a mean of $600 and a standard deviation of $60. If sales are $540, what is the value of z?

A credit card company found that its customers charge between $100 and $1,100 per month. If this random variable is uniformly distributed, the standard deviation of the monthly amount charged equals $____. Round your answer to the nearest cent.

A clothing store analyzed customer purchases over the past year and found them to be normally distributed with a mean of $110 and a standard deviation of $12. The probability that a randomly selected person spent between $87 and $138 at the store last year is ____% Round to two decimals.

A credit card company found that its customers charge between $100 and $1,100 per month. If monthly amount charged is uniformly distributed, the probability that a person charges less than $200 per month is ____%

An economics professor gives an A grade to any student scoring in the top 8.5% of her Principles of Economics class. If the scores are normally distributed with a mean of 70% and a standard deviation of 5%, the minimum grade a student must score to receive a grade of A is _____%. Round to two decimal places.

A random survey of adult Canadians indicated that the mean number of hours spent watching television per week was 9 with a standard deviation of 1.5 hours. If hours watching television per week is a normally distributed variable, the probability of randomly selecting a Canadian adult and finding that they watch somewhere between 10 and 12 hours of television per week is ____%. Round your answer to 2 decimal places.

The mean cholesterol level of 40 to 60-year-old women surveyed in a particular country was found to be 5 mmol/l with a standard deviation is 1 mmol/l. About 4% of all women in this age category would have a cholesterol level below _____ mmol/l? Leave two decimal places in your answer.

Suppose a train arrives at a stop every 30 minutes between 5 a.m. and 11:30 p.m. The time that a passenger will wait for the train is uniformly distributed from 0 to 30 minutes. The probability a passenger will wait more than 25 minutes is ____%. Round your answer to 2 decimal places.

Answer 1

1) µ=   600
σ=   60

Z=(X-µ)/σ=   (540-600)/60)=       -1

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2)

it is uniform distribution   
  
here a=   100
b=   1100

variance =    (b-a)²/12 =    83333.33333
      
std dev =   √ variance =    288.68

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µ =    110                                  
σ =    12                                  
we need to calculate probability for ,                                      
P (   87   < X <   138   )                      
=P( (87-110)/12 < (X-µ)/σ < (138-110)/12 )                                      
                                      
P (    -1.917   < Z <    2.333   )                       
= P ( Z <    2.333   ) - P ( Z <   -1.917   ) =    0.9902   -    0.0276   =    0.9625 or 96.25%(answer)
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it is uniform distribution   
  
here a=   100
b=   1100
P(X ≤ 200) =    (x-a)/(b-a) = (200-100)/(1100-100) = 0.100 or 10.00%