Question

Question 1: The amount that people spend per month on entertainment follows a normal distribution with a mean of $175 and a standard deviation of $40 what is the probability that a person spends less than $149.80 per month on entertainment. (Round to four decimal places)

Question 2: The amount of pickles in a jar is normally distributed with μ= 110 grams and σ= 25 grams. A sample of 25 jars has to be selected, what is the probability that the sample mean will be between 100 and 120 grams (Round to four decimal places)

Please show all work/calculations needed for these 2 questions

Answer 1

Solution :

Given that,

mean = = 175

standard deviation = =  40

P(X< 149.80) = P[(X- ) / < (149.80 - 175) /40 ]

= P(z <-0.63 )

Using z table

= 0.2643

b.

Given that ,

mean =   = 110

standard deviation = = 25

n = 25

= 110

=  / n= 25/ 25=5

P(100<     <120 ) = P[(100-110) / 5< ( - ) /   < (120-110) /5 )]

= P(-2 < Z < 2)

= P(Z <2 ) - P(Z <-2 )

Using z table

=0.9772-0.0228

=0.9544

probability