At a local sandwich shop the average customer spends $25 at dinner with a standard deviation of $2.30. In a simple random sample of 40 customers, what is the probability that the mean receipt for dinner is between $24.50 and $25.50

The probability that the mean receipt for dinner is between $24.50 and $25.50 is

P(24.50≤ x ≤ 25.50)= 0.8324

Step-by-step explanation:

Step(i):-

Given mean of Population(μ) = $25

Given standard deviation of the Population  (σ) = 2.30

Sample size 'n' = 40

Let 'X' be the random variable in normal distribution

Given X₁ = 24.50

Given X₂ = 25.50

Step(ii):-

The probability that the mean receipt for dinner is between $24.50 and $25.50

P(x₁≤ x ≤ x₂) = P(Z₁≤ z ≤ Z₂) = A(Z₂) + A(z₁)

P(24.50≤ x ≤ 25.50) = P(-1.375≤ z ≤ 1.375) = A(1.375) + A(1.375)

P(24.50≤ x ≤ 25.50)= 2 A( 1.375)

                               = 2 × 0.4162 ( from normal table)

                              = 0.8324

Final answer:-

The probability that the mean receipt for dinner is between $24.50 and $25.50 is 0.8324

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!